diff --git a/django/db/backends/base/schema.py b/django/db/backends/base/schema.py
index adaf6d7378..ef915c311b 100644
--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -1184,16 +1184,16 @@ class BaseDatabaseSchemaEditor:
 
     def _unique_sql(
         self, model, fields, name, condition=None, deferrable=None,
-        include=None, opclasses=None,
+        include=None, opclasses=None, expressions=None,
     ):
         if (
             deferrable and
             not self.connection.features.supports_deferrable_unique_constraints
         ):
             return None
-        if condition or include or opclasses:
-            # Databases support conditional and covering unique constraints via
-            # a unique index.
+        if condition or include or opclasses or expressions:
+            # Databases support conditional, covering, and functional unique
+            # constraints via a unique index.
             sql = self._create_unique_sql(
                 model,
                 fields,
@@ -1201,6 +1201,7 @@ class BaseDatabaseSchemaEditor:
                 condition=condition,
                 include=include,
                 opclasses=opclasses,
+                expressions=expressions,
             )
             if sql:
                 self.deferred_sql.append(sql)
@@ -1216,7 +1217,7 @@ class BaseDatabaseSchemaEditor:
 
     def _create_unique_sql(
         self, model, columns, name=None, condition=None, deferrable=None,
-        include=None, opclasses=None,
+        include=None, opclasses=None, expressions=None,
     ):
         if (
             (
@@ -1224,23 +1225,28 @@ class BaseDatabaseSchemaEditor:
                 not self.connection.features.supports_deferrable_unique_constraints
             ) or
             (condition and not self.connection.features.supports_partial_indexes) or
-            (include and not self.connection.features.supports_covering_indexes)
+            (include and not self.connection.features.supports_covering_indexes) or
+            (expressions and not self.connection.features.supports_expression_indexes)
         ):
             return None
 
         def create_unique_name(*args, **kwargs):
             return self.quote_name(self._create_index_name(*args, **kwargs))
 
+        compiler = Query(model, alias_cols=False).get_compiler(connection=self.connection)
         table = Table(model._meta.db_table, self.quote_name)
         if name is None:
             name = IndexName(model._meta.db_table, columns, '_uniq', create_unique_name)
         else:
             name = self.quote_name(name)
-        columns = self._index_columns(table, columns, col_suffixes=(), opclasses=opclasses)
-        if condition or include or opclasses:
+        if condition or include or opclasses or expressions:
             sql = self.sql_create_unique_index
         else:
             sql = self.sql_create_unique
+        if columns:
+            columns = self._index_columns(table, columns, col_suffixes=(), opclasses=opclasses)
+        else:
+            columns = Expressions(model._meta.db_table, expressions, compiler, self.quote_value)
         return Statement(
             sql,
             table=table,
@@ -1253,7 +1259,7 @@ class BaseDatabaseSchemaEditor:
 
     def _delete_unique_sql(
         self, model, name, condition=None, deferrable=None, include=None,
-        opclasses=None,
+        opclasses=None, expressions=None,
     ):
         if (
             (
@@ -1261,10 +1267,12 @@ class BaseDatabaseSchemaEditor:
                 not self.connection.features.supports_deferrable_unique_constraints
             ) or
             (condition and not self.connection.features.supports_partial_indexes) or
-            (include and not self.connection.features.supports_covering_indexes)
+            (include and not self.connection.features.supports_covering_indexes) or
+            (expressions and not self.connection.features.supports_expression_indexes)
+
         ):
             return None
-        if condition or include or opclasses:
+        if condition or include or opclasses or expressions:
             sql = self.sql_delete_index
         else:
             sql = self.sql_delete_unique
diff --git a/django/db/backends/mysql/introspection.py b/django/db/backends/mysql/introspection.py
index 346765e30a..cd3e13eebe 100644
--- a/django/db/backends/mysql/introspection.py
+++ b/django/db/backends/mysql/introspection.py
@@ -289,7 +289,7 @@ class DatabaseIntrospection(BaseDatabaseIntrospection):
                 constraints[index] = {
                     'columns': OrderedSet(),
                     'primary_key': False,
-                    'unique': False,
+                    'unique': not non_unique,
                     'check': False,
                     'foreign_key': None,
                 }
diff --git a/django/db/backends/oracle/introspection.py b/django/db/backends/oracle/introspection.py
index a5df7f1297..fa7a34ed0a 100644
--- a/django/db/backends/oracle/introspection.py
+++ b/django/db/backends/oracle/introspection.py
@@ -307,6 +307,7 @@ class DatabaseIntrospection(BaseDatabaseIntrospection):
             SELECT
                 ind.index_name,
                 LOWER(ind.index_type),
+                LOWER(ind.uniqueness),
                 LISTAGG(LOWER(cols.column_name), ',') WITHIN GROUP (ORDER BY cols.column_position),
                 LISTAGG(cols.descend, ',') WITHIN GROUP (ORDER BY cols.column_position)
             FROM
@@ -318,13 +319,13 @@ class DatabaseIntrospection(BaseDatabaseIntrospection):
                     FROM user_constraints cons
                     WHERE ind.index_name = cons.index_name
                 ) AND cols.index_name = ind.index_name
-            GROUP BY ind.index_name, ind.index_type
+            GROUP BY ind.index_name, ind.index_type, ind.uniqueness
         """, [table_name])
-        for constraint, type_, columns, orders in cursor.fetchall():
+        for constraint, type_, unique, columns, orders in cursor.fetchall():
             constraint = self.identifier_converter(constraint)
             constraints[constraint] = {
                 'primary_key': False,
-                'unique': False,
+                'unique': unique == 'unique',
                 'foreign_key': None,
                 'check': False,
                 'index': True,
diff --git a/django/db/backends/sqlite3/schema.py b/django/db/backends/sqlite3/schema.py
index 6a2c887612..b089a9d355 100644
--- a/django/db/backends/sqlite3/schema.py
+++ b/django/db/backends/sqlite3/schema.py
@@ -419,13 +419,17 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
         self.delete_model(old_field.remote_field.through)
 
     def add_constraint(self, model, constraint):
-        if isinstance(constraint, UniqueConstraint) and constraint.condition:
+        if isinstance(constraint, UniqueConstraint) and (
+            constraint.condition or constraint.contains_expressions
+        ):
             super().add_constraint(model, constraint)
         else:
             self._remake_table(model)
 
     def remove_constraint(self, model, constraint):
-        if isinstance(constraint, UniqueConstraint) and constraint.condition:
+        if isinstance(constraint, UniqueConstraint) and (
+            constraint.condition or constraint.contains_expressions
+        ):
             super().remove_constraint(model, constraint)
         else:
             self._remake_table(model)
diff --git a/django/db/models/base.py b/django/db/models/base.py
index fd8e0806b1..27c9ff6461 100644
--- a/django/db/models/base.py
+++ b/django/db/models/base.py
@@ -2039,6 +2039,25 @@ class Model(metaclass=ModelBase):
                         id='models.W039',
                     )
                 )
+            if not (
+                connection.features.supports_expression_indexes or
+                'supports_expression_indexes' in cls._meta.required_db_features
+            ) and any(
+                isinstance(constraint, UniqueConstraint) and constraint.contains_expressions
+                for constraint in cls._meta.constraints
+            ):
+                errors.append(
+                    checks.Warning(
+                        '%s does not support unique constraints on '
+                        'expressions.' % connection.display_name,
+                        hint=(
+                            "A constraint won't be created. Silence this "
+                            "warning if you don't care about it."
+                        ),
+                        obj=cls,
+                        id='models.W044',
+                    )
+                )
             fields = set(chain.from_iterable(
                 (*constraint.fields, *constraint.include)
                 for constraint in cls._meta.constraints if isinstance(constraint, UniqueConstraint)
@@ -2051,6 +2070,12 @@ class Model(metaclass=ModelBase):
                         'supports_partial_indexes' not in cls._meta.required_db_features
                     ) and isinstance(constraint.condition, Q):
                         references.update(cls._get_expr_references(constraint.condition))
+                    if (
+                        connection.features.supports_expression_indexes or
+                        'supports_expression_indexes' not in cls._meta.required_db_features
+                    ) and constraint.contains_expressions:
+                        for expression in constraint.expressions:
+                            references.update(cls._get_expr_references(expression))
                 elif isinstance(constraint, CheckConstraint):
                     if (
                         connection.features.supports_table_check_constraints or
diff --git a/django/db/models/constraints.py b/django/db/models/constraints.py
index 0b85b46257..b073df1763 100644
--- a/django/db/models/constraints.py
+++ b/django/db/models/constraints.py
@@ -1,5 +1,7 @@
 from enum import Enum
 
+from django.db.models.expressions import ExpressionList, F
+from django.db.models.indexes import IndexExpression
 from django.db.models.query_utils import Q
 from django.db.models.sql.query import Query
 
@@ -10,6 +12,10 @@ class BaseConstraint:
     def __init__(self, name):
         self.name = name
 
+    @property
+    def contains_expressions(self):
+        return False
+
     def constraint_sql(self, model, schema_editor):
         raise NotImplementedError('This method must be implemented by a subclass.')
 
@@ -83,16 +89,25 @@ class Deferrable(Enum):
 class UniqueConstraint(BaseConstraint):
     def __init__(
         self,
-        *,
-        fields,
-        name,
+        *expressions,
+        fields=(),
+        name=None,
         condition=None,
         deferrable=None,
         include=None,
         opclasses=(),
     ):
-        if not fields:
-            raise ValueError('At least one field is required to define a unique constraint.')
+        if not name:
+            raise ValueError('A unique constraint must be named.')
+        if not expressions and not fields:
+            raise ValueError(
+                'At least one field or expression is required to define a '
+                'unique constraint.'
+            )
+        if expressions and fields:
+            raise ValueError(
+                'UniqueConstraint.fields and expressions are mutually exclusive.'
+            )
         if not isinstance(condition, (type(None), Q)):
             raise ValueError('UniqueConstraint.condition must be a Q instance.')
         if condition and deferrable:
@@ -107,6 +122,15 @@ class UniqueConstraint(BaseConstraint):
             raise ValueError(
                 'UniqueConstraint with opclasses cannot be deferred.'
             )
+        if expressions and deferrable:
+            raise ValueError(
+                'UniqueConstraint with expressions cannot be deferred.'
+            )
+        if expressions and opclasses:
+            raise ValueError(
+                'UniqueConstraint.opclasses cannot be used with expressions. '
+                'Use django.contrib.postgres.indexes.OpClass() instead.'
+            )
         if not isinstance(deferrable, (type(None), Deferrable)):
             raise ValueError(
                 'UniqueConstraint.deferrable must be a Deferrable instance.'
@@ -125,8 +149,16 @@ class UniqueConstraint(BaseConstraint):
         self.deferrable = deferrable
         self.include = tuple(include) if include else ()
         self.opclasses = opclasses
+        self.expressions = tuple(
+            F(expression) if isinstance(expression, str) else expression
+            for expression in expressions
+        )
         super().__init__(name)
 
+    @property
+    def contains_expressions(self):
+        return bool(self.expressions)
+
     def _get_condition_sql(self, model, schema_editor):
         if self.condition is None:
             return None
@@ -136,39 +168,55 @@ class UniqueConstraint(BaseConstraint):
         sql, params = where.as_sql(compiler, schema_editor.connection)
         return sql % tuple(schema_editor.quote_value(p) for p in params)
 
+    def _get_index_expressions(self, model, schema_editor):
+        if not self.expressions:
+            return None
+        index_expressions = []
+        for expression in self.expressions:
+            index_expression = IndexExpression(expression)
+            index_expression.set_wrapper_classes(schema_editor.connection)
+            index_expressions.append(index_expression)
+        return ExpressionList(*index_expressions).resolve_expression(
+            Query(model, alias_cols=False),
+        )
+
     def constraint_sql(self, model, schema_editor):
         fields = [model._meta.get_field(field_name).column for field_name in self.fields]
         include = [model._meta.get_field(field_name).column for field_name in self.include]
         condition = self._get_condition_sql(model, schema_editor)
+        expressions = self._get_index_expressions(model, schema_editor)
         return schema_editor._unique_sql(
             model, fields, self.name, condition=condition,
             deferrable=self.deferrable, include=include,
-            opclasses=self.opclasses,
+            opclasses=self.opclasses, expressions=expressions,
         )
 
     def create_sql(self, model, schema_editor):
         fields = [model._meta.get_field(field_name).column for field_name in self.fields]
         include = [model._meta.get_field(field_name).column for field_name in self.include]
         condition = self._get_condition_sql(model, schema_editor)
+        expressions = self._get_index_expressions(model, schema_editor)
         return schema_editor._create_unique_sql(
             model, fields, self.name, condition=condition,
             deferrable=self.deferrable, include=include,
-            opclasses=self.opclasses,
+            opclasses=self.opclasses, expressions=expressions,
         )
 
     def remove_sql(self, model, schema_editor):
         condition = self._get_condition_sql(model, schema_editor)
         include = [model._meta.get_field(field_name).column for field_name in self.include]
+        expressions = self._get_index_expressions(model, schema_editor)
         return schema_editor._delete_unique_sql(
             model, self.name, condition=condition, deferrable=self.deferrable,
-            include=include, opclasses=self.opclasses,
+            include=include, opclasses=self.opclasses, expressions=expressions,
         )
 
     def __repr__(self):
-        return '<%s: fields=%s name=%s%s%s%s%s>' % (
+        return '<%s:%s%s%s%s%s%s%s>' % (
             self.__class__.__qualname__,
-            repr(self.fields),
-            repr(self.name),
+            '' if not self.fields else ' fields=%s' % repr(self.fields),
+            '' if not self.expressions else ' expressions=%s' % repr(self.expressions),
+            ' name=%s' % repr(self.name),
             '' if self.condition is None else ' condition=%s' % self.condition,
             '' if self.deferrable is None else ' deferrable=%s' % self.deferrable,
             '' if not self.include else ' include=%s' % repr(self.include),
@@ -183,13 +231,15 @@ class UniqueConstraint(BaseConstraint):
                 self.condition == other.condition and
                 self.deferrable == other.deferrable and
                 self.include == other.include and
-                self.opclasses == other.opclasses
+                self.opclasses == other.opclasses and
+                self.expressions == other.expressions
             )
         return super().__eq__(other)
 
     def deconstruct(self):
         path, args, kwargs = super().deconstruct()
-        kwargs['fields'] = self.fields
+        if self.fields:
+            kwargs['fields'] = self.fields
         if self.condition:
             kwargs['condition'] = self.condition
         if self.deferrable:
@@ -198,4 +248,4 @@ class UniqueConstraint(BaseConstraint):
             kwargs['include'] = self.include
         if self.opclasses:
             kwargs['opclasses'] = self.opclasses
-        return path, args, kwargs
+        return path, self.expressions, kwargs
diff --git a/docs/ref/checks.txt b/docs/ref/checks.txt
index 7761a2a323..dbba801e39 100644
--- a/docs/ref/checks.txt
+++ b/docs/ref/checks.txt
@@ -391,6 +391,8 @@ Models
 * **models.W042**: Auto-created primary key used when not defining a primary
   key type, by default ``django.db.models.AutoField``.
 * **models.W043**: ``<database>`` does not support indexes on expressions.
+* **models.W044**: ``<database>`` does not support unique constraints on
+  expressions.
 
 Security
 --------
diff --git a/docs/ref/contrib/postgres/indexes.txt b/docs/ref/contrib/postgres/indexes.txt
index b6a4aba808..9a9b7fc73b 100644
--- a/docs/ref/contrib/postgres/indexes.txt
+++ b/docs/ref/contrib/postgres/indexes.txt
@@ -183,10 +183,10 @@ available from the ``django.contrib.postgres.indexes`` module.
 .. class:: OpClass(expression, name)
 
     An ``OpClass()`` expression represents the ``expression`` with a custom
-    `operator class`_ that can be used to define functional indexes. To use it,
-    you need to add ``'django.contrib.postgres'`` in your
-    :setting:`INSTALLED_APPS`. Set the ``name`` parameter to the name of the
-    `operator class`_.
+    `operator class`_ that can be used to define functional indexes or unique
+    constraints. To use it, you need to add ``'django.contrib.postgres'`` in
+    your :setting:`INSTALLED_APPS`. Set the ``name`` parameter to the name of
+    the `operator class`_.
 
     For example::
 
@@ -197,4 +197,18 @@ available from the ``django.contrib.postgres.indexes`` module.
 
     creates an index on ``Lower('username')`` using ``varchar_pattern_ops``.
 
+    Another example::
+
+        UniqueConstraint(
+            OpClass(Upper('description'), name='text_pattern_ops'),
+            name='upper_description_unique',
+        )
+
+    creates a unique constraint on ``Upper('description')`` using
+    ``text_pattern_ops``.
+
+    .. versionchanged:: 4.0
+
+        Support for functional unique constraints was added.
+
     .. _operator class: https://www.postgresql.org/docs/current/indexes-opclass.html
diff --git a/docs/ref/models/constraints.txt b/docs/ref/models/constraints.txt
index e3b682d1c5..c675903db6 100644
--- a/docs/ref/models/constraints.txt
+++ b/docs/ref/models/constraints.txt
@@ -69,10 +69,30 @@ constraint.
 ``UniqueConstraint``
 ====================
 
-.. class:: UniqueConstraint(*, fields, name, condition=None, deferrable=None, include=None, opclasses=())
+.. class:: UniqueConstraint(*expressions, fields=(), name=None, condition=None, deferrable=None, include=None, opclasses=())
 
     Creates a unique constraint in the database.
 
+``expressions``
+---------------
+
+.. attribute:: UniqueConstraint.expressions
+
+.. versionadded:: 4.0
+
+Positional argument ``*expressions`` allows creating functional unique
+constraints on expressions and database functions.
+
+For example::
+
+    UniqueConstraint(Lower('name').desc(), 'category', name='unique_lower_name_category')
+
+creates a unique constraint on the lowercased value of the ``name`` field in
+descending order and the ``category`` field in the default ascending order.
+
+Functional unique constraints have the same database restrictions as
+:attr:`Index.expressions`.
+
 ``fields``
 ----------
 
diff --git a/docs/releases/4.0.txt b/docs/releases/4.0.txt
index f1a25d0d92..502aabd4d1 100644
--- a/docs/releases/4.0.txt
+++ b/docs/releases/4.0.txt
@@ -28,6 +28,36 @@ The Django 3.2.x series is the last to support Python 3.6 and 3.7.
 What's new in Django 4.0
 ========================
 
+Functional unique constraints
+-----------------------------
+
+The new :attr:`*expressions <django.db.models.UniqueConstraint.expressions>`
+positional argument of
+:class:`UniqueConstraint() <django.db.models.UniqueConstraint>` enables
+creating functional unique constraints on expressions and database functions.
+For example::
+
+    from django.db import models
+    from django.db.models import UniqueConstraint
+    from django.db.models.functions import Lower
+
+
+    class MyModel(models.Model):
+        first_name = models.CharField(max_length=255)
+        last_name = models.CharField(max_length=255)
+
+        class Meta:
+            indexes = [
+                UniqueConstraint(
+                    Lower('first_name'),
+                    Lower('last_name').desc(),
+                    name='first_last_name_unique',
+                ),
+            ]
+
+Functional unique constraints are added to models using the
+:attr:`Meta.constraints <django.db.models.Options.constraints>` option.
+
 Minor features
 --------------
 
diff --git a/tests/constraints/tests.py b/tests/constraints/tests.py
index cb366d8e45..3d59d07b24 100644
--- a/tests/constraints/tests.py
+++ b/tests/constraints/tests.py
@@ -2,7 +2,9 @@ from unittest import mock
 
 from django.core.exceptions import ValidationError
 from django.db import IntegrityError, connection, models
+from django.db.models import F
 from django.db.models.constraints import BaseConstraint
+from django.db.models.functions import Lower
 from django.db.transaction import atomic
 from django.test import SimpleTestCase, TestCase, skipUnlessDBFeature
 
@@ -25,6 +27,10 @@ class BaseConstraintTests(SimpleTestCase):
         with self.assertRaisesMessage(NotImplementedError, msg):
             c.constraint_sql(None, None)
 
+    def test_contains_expressions(self):
+        c = BaseConstraint('name')
+        self.assertIs(c.contains_expressions, False)
+
     def test_create_sql(self):
         c = BaseConstraint('name')
         msg = 'This method must be implemented by a subclass.'
@@ -218,6 +224,25 @@ class UniqueConstraintTests(TestCase):
         self.assertEqual(constraint_1, constraint_1)
         self.assertNotEqual(constraint_1, constraint_2)
 
+    def test_eq_with_expressions(self):
+        constraint = models.UniqueConstraint(
+            Lower('title'),
+            F('author'),
+            name='book_func_uq',
+        )
+        same_constraint = models.UniqueConstraint(
+            Lower('title'),
+            'author',
+            name='book_func_uq',
+        )
+        another_constraint = models.UniqueConstraint(
+            Lower('title'),
+            name='book_func_uq',
+        )
+        self.assertEqual(constraint, same_constraint)
+        self.assertEqual(constraint, mock.ANY)
+        self.assertNotEqual(constraint, another_constraint)
+
     def test_repr(self):
         fields = ['foo', 'bar']
         name = 'unique_fields'
@@ -275,6 +300,18 @@ class UniqueConstraintTests(TestCase):
             "opclasses=['text_pattern_ops', 'varchar_pattern_ops']>",
         )
 
+    def test_repr_with_expressions(self):
+        constraint = models.UniqueConstraint(
+            Lower('title'),
+            F('author'),
+            name='book_func_uq',
+        )
+        self.assertEqual(
+            repr(constraint),
+            "<UniqueConstraint: expressions=(Lower(F(title)), F(author)) "
+            "name='book_func_uq'>",
+        )
+
     def test_deconstruction(self):
         fields = ['foo', 'bar']
         name = 'unique_fields'
@@ -339,6 +376,14 @@ class UniqueConstraintTests(TestCase):
             'opclasses': opclasses,
         })
 
+    def test_deconstruction_with_expressions(self):
+        name = 'unique_fields'
+        constraint = models.UniqueConstraint(Lower('title'), name=name)
+        path, args, kwargs = constraint.deconstruct()
+        self.assertEqual(path, 'django.db.models.UniqueConstraint')
+        self.assertEqual(args, (Lower('title'),))
+        self.assertEqual(kwargs, {'name': name})
+
     def test_database_constraint(self):
         with self.assertRaises(IntegrityError):
             UniqueConstraintProduct.objects.create(name=self.p1.name, color=self.p1.color)
@@ -434,6 +479,15 @@ class UniqueConstraintTests(TestCase):
                 deferrable=models.Deferrable.DEFERRED,
             )
 
+    def test_deferrable_with_expressions(self):
+        message = 'UniqueConstraint with expressions cannot be deferred.'
+        with self.assertRaisesMessage(ValueError, message):
+            models.UniqueConstraint(
+                Lower('name'),
+                name='deferred_expression_unique',
+                deferrable=models.Deferrable.DEFERRED,
+            )
+
     def test_invalid_defer_argument(self):
         message = 'UniqueConstraint.deferrable must be a Deferrable instance.'
         with self.assertRaisesMessage(ValueError, message):
@@ -481,3 +535,33 @@ class UniqueConstraintTests(TestCase):
                 fields=['field'],
                 opclasses=['foo', 'bar'],
             )
+
+    def test_requires_field_or_expression(self):
+        msg = (
+            'At least one field or expression is required to define a unique '
+            'constraint.'
+        )
+        with self.assertRaisesMessage(ValueError, msg):
+            models.UniqueConstraint(name='name')
+
+    def test_expressions_and_fields_mutually_exclusive(self):
+        msg = 'UniqueConstraint.fields and expressions are mutually exclusive.'
+        with self.assertRaisesMessage(ValueError, msg):
+            models.UniqueConstraint(Lower('field_1'), fields=['field_2'], name='name')
+
+    def test_expressions_with_opclasses(self):
+        msg = (
+            'UniqueConstraint.opclasses cannot be used with expressions. Use '
+            'django.contrib.postgres.indexes.OpClass() instead.'
+        )
+        with self.assertRaisesMessage(ValueError, msg):
+            models.UniqueConstraint(
+                Lower('field'),
+                name='test_func_opclass',
+                opclasses=['jsonb_path_ops'],
+            )
+
+    def test_requires_name(self):
+        msg = 'A unique constraint must be named.'
+        with self.assertRaisesMessage(ValueError, msg):
+            models.UniqueConstraint(fields=['field'])
diff --git a/tests/invalid_models_tests/test_models.py b/tests/invalid_models_tests/test_models.py
index b20eef7159..c79684487d 100644
--- a/tests/invalid_models_tests/test_models.py
+++ b/tests/invalid_models_tests/test_models.py
@@ -2178,3 +2178,144 @@ class ConstraintsTests(TestCase):
                 ]
 
         self.assertEqual(Model.check(databases=self.databases), [])
+
+    def test_func_unique_constraint(self):
+        class Model(models.Model):
+            name = models.CharField(max_length=10)
+
+            class Meta:
+                constraints = [
+                    models.UniqueConstraint(Lower('name'), name='lower_name_uq'),
+                ]
+
+        warn = Warning(
+            '%s does not support unique constraints on expressions.'
+            % connection.display_name,
+            hint=(
+                "A constraint won't be created. Silence this warning if you "
+                "don't care about it."
+            ),
+            obj=Model,
+            id='models.W044',
+        )
+        expected = [] if connection.features.supports_expression_indexes else [warn]
+        self.assertEqual(Model.check(databases=self.databases), expected)
+
+    def test_func_unique_constraint_required_db_features(self):
+        class Model(models.Model):
+            name = models.CharField(max_length=10)
+
+            class Meta:
+                constraints = [
+                    models.UniqueConstraint(Lower('name'), name='lower_name_unq'),
+                ]
+                required_db_features = {'supports_expression_indexes'}
+
+        self.assertEqual(Model.check(databases=self.databases), [])
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_expression_custom_lookup(self):
+        class Model(models.Model):
+            height = models.IntegerField()
+            weight = models.IntegerField()
+
+            class Meta:
+                constraints = [
+                    models.UniqueConstraint(
+                        models.F('height') / (models.F('weight__abs') + models.Value(5)),
+                        name='name',
+                    ),
+                ]
+
+        with register_lookup(models.IntegerField, Abs):
+            self.assertEqual(Model.check(databases=self.databases), [])
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_pointing_to_missing_field(self):
+        class Model(models.Model):
+            class Meta:
+                constraints = [
+                    models.UniqueConstraint(Lower('missing_field').desc(), name='name'),
+                ]
+
+        self.assertEqual(Model.check(databases=self.databases), [
+            Error(
+                "'constraints' refers to the nonexistent field "
+                "'missing_field'.",
+                obj=Model,
+                id='models.E012',
+            ),
+        ])
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_pointing_to_missing_field_nested(self):
+        class Model(models.Model):
+            class Meta:
+                constraints = [
+                    models.UniqueConstraint(Abs(Round('missing_field')), name='name'),
+                ]
+
+        self.assertEqual(Model.check(databases=self.databases), [
+            Error(
+                "'constraints' refers to the nonexistent field "
+                "'missing_field'.",
+                obj=Model,
+                id='models.E012',
+            ),
+        ])
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_pointing_to_m2m_field(self):
+        class Model(models.Model):
+            m2m = models.ManyToManyField('self')
+
+            class Meta:
+                constraints = [models.UniqueConstraint(Lower('m2m'), name='name')]
+
+        self.assertEqual(Model.check(databases=self.databases), [
+            Error(
+                "'constraints' refers to a ManyToManyField 'm2m', but "
+                "ManyToManyFields are not permitted in 'constraints'.",
+                obj=Model,
+                id='models.E013',
+            ),
+        ])
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_pointing_to_non_local_field(self):
+        class Foo(models.Model):
+            field1 = models.CharField(max_length=15)
+
+        class Bar(Foo):
+            class Meta:
+                constraints = [models.UniqueConstraint(Lower('field1'), name='name')]
+
+        self.assertEqual(Bar.check(databases=self.databases), [
+            Error(
+                "'constraints' refers to field 'field1' which is not local to "
+                "model 'Bar'.",
+                hint='This issue may be caused by multi-table inheritance.',
+                obj=Bar,
+                id='models.E016',
+            ),
+        ])
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_pointing_to_fk(self):
+        class Foo(models.Model):
+            id = models.CharField(primary_key=True, max_length=255)
+
+        class Bar(models.Model):
+            foo_1 = models.ForeignKey(Foo, models.CASCADE, related_name='bar_1')
+            foo_2 = models.ForeignKey(Foo, models.CASCADE, related_name='bar_2')
+
+            class Meta:
+                constraints = [
+                    models.UniqueConstraint(
+                        Lower('foo_1_id'),
+                        Lower('foo_2'),
+                        name='name',
+                    ),
+                ]
+
+        self.assertEqual(Bar.check(databases=self.databases), [])
diff --git a/tests/migrations/test_operations.py b/tests/migrations/test_operations.py
index 73a0c63921..cbd65bdb37 100644
--- a/tests/migrations/test_operations.py
+++ b/tests/migrations/test_operations.py
@@ -2562,6 +2562,99 @@ class OperationTests(OperationTestBase):
             'name': 'covering_pink_constraint_rm',
         })
 
+    def test_add_func_unique_constraint(self):
+        app_label = 'test_adfuncuc'
+        constraint_name = f'{app_label}_pony_abs_uq'
+        table_name = f'{app_label}_pony'
+        project_state = self.set_up_test_model(app_label)
+        constraint = models.UniqueConstraint(Abs('weight'), name=constraint_name)
+        operation = migrations.AddConstraint('Pony', constraint)
+        self.assertEqual(
+            operation.describe(),
+            'Create constraint test_adfuncuc_pony_abs_uq on model Pony',
+        )
+        self.assertEqual(
+            operation.migration_name_fragment,
+            'pony_test_adfuncuc_pony_abs_uq',
+        )
+        new_state = project_state.clone()
+        operation.state_forwards(app_label, new_state)
+        self.assertEqual(len(new_state.models[app_label, 'pony'].options['constraints']), 1)
+        self.assertIndexNameNotExists(table_name, constraint_name)
+        # Add constraint.
+        with connection.schema_editor() as editor:
+            operation.database_forwards(app_label, editor, project_state, new_state)
+        Pony = new_state.apps.get_model(app_label, 'Pony')
+        Pony.objects.create(weight=4.0)
+        if connection.features.supports_expression_indexes:
+            self.assertIndexNameExists(table_name, constraint_name)
+            with self.assertRaises(IntegrityError):
+                Pony.objects.create(weight=-4.0)
+        else:
+            self.assertIndexNameNotExists(table_name, constraint_name)
+            Pony.objects.create(weight=-4.0)
+        # Reversal.
+        with connection.schema_editor() as editor:
+            operation.database_backwards(app_label, editor, new_state, project_state)
+        self.assertIndexNameNotExists(table_name, constraint_name)
+        # Constraint doesn't work.
+        Pony.objects.create(weight=-4.0)
+        # Deconstruction.
+        definition = operation.deconstruct()
+        self.assertEqual(definition[0], 'AddConstraint')
+        self.assertEqual(definition[1], [])
+        self.assertEqual(
+            definition[2],
+            {'model_name': 'Pony', 'constraint': constraint},
+        )
+
+    def test_remove_func_unique_constraint(self):
+        app_label = 'test_rmfuncuc'
+        constraint_name = f'{app_label}_pony_abs_uq'
+        table_name = f'{app_label}_pony'
+        project_state = self.set_up_test_model(app_label, constraints=[
+            models.UniqueConstraint(Abs('weight'), name=constraint_name),
+        ])
+        self.assertTableExists(table_name)
+        if connection.features.supports_expression_indexes:
+            self.assertIndexNameExists(table_name, constraint_name)
+        operation = migrations.RemoveConstraint('Pony', constraint_name)
+        self.assertEqual(
+            operation.describe(),
+            'Remove constraint test_rmfuncuc_pony_abs_uq from model Pony',
+        )
+        self.assertEqual(
+            operation.migration_name_fragment,
+            'remove_pony_test_rmfuncuc_pony_abs_uq',
+        )
+        new_state = project_state.clone()
+        operation.state_forwards(app_label, new_state)
+        self.assertEqual(len(new_state.models[app_label, 'pony'].options['constraints']), 0)
+        Pony = new_state.apps.get_model(app_label, 'Pony')
+        self.assertEqual(len(Pony._meta.constraints), 0)
+        # Remove constraint.
+        with connection.schema_editor() as editor:
+            operation.database_forwards(app_label, editor, project_state, new_state)
+        self.assertIndexNameNotExists(table_name, constraint_name)
+        # Constraint doesn't work.
+        Pony.objects.create(pink=1, weight=4.0)
+        Pony.objects.create(pink=1, weight=-4.0).delete()
+        # Reversal.
+        with connection.schema_editor() as editor:
+            operation.database_backwards(app_label, editor, new_state, project_state)
+        if connection.features.supports_expression_indexes:
+            self.assertIndexNameExists(table_name, constraint_name)
+            with self.assertRaises(IntegrityError):
+                Pony.objects.create(weight=-4.0)
+        else:
+            self.assertIndexNameNotExists(table_name, constraint_name)
+            Pony.objects.create(weight=-4.0)
+        # Deconstruction.
+        definition = operation.deconstruct()
+        self.assertEqual(definition[0], 'RemoveConstraint')
+        self.assertEqual(definition[1], [])
+        self.assertEqual(definition[2], {'model_name': 'Pony', 'name': constraint_name})
+
     def test_alter_model_options(self):
         """
         Tests the AlterModelOptions operation.
diff --git a/tests/postgres_tests/test_constraints.py b/tests/postgres_tests/test_constraints.py
index 80c2bb77b6..7915bb226e 100644
--- a/tests/postgres_tests/test_constraints.py
+++ b/tests/postgres_tests/test_constraints.py
@@ -1,6 +1,7 @@
 import datetime
 from unittest import mock
 
+from django.contrib.postgres.indexes import OpClass
 from django.db import (
     IntegrityError, NotSupportedError, connection, transaction,
 )
@@ -8,8 +9,8 @@ from django.db.models import (
     CheckConstraint, Deferrable, F, Func, IntegerField, Q, UniqueConstraint,
 )
 from django.db.models.fields.json import KeyTextTransform
-from django.db.models.functions import Cast, Left
-from django.test import skipUnlessDBFeature
+from django.db.models.functions import Cast, Left, Lower
+from django.test import modify_settings, skipUnlessDBFeature
 from django.utils import timezone
 
 from . import PostgreSQLTestCase
@@ -26,6 +27,7 @@ except ImportError:
     pass
 
 
+@modify_settings(INSTALLED_APPS={'append': 'django.contrib.postgres'})
 class SchemaTests(PostgreSQLTestCase):
     get_opclass_query = '''
         SELECT opcname, c.relname FROM pg_opclass AS oc
@@ -166,6 +168,33 @@ class SchemaTests(PostgreSQLTestCase):
                 [('varchar_pattern_ops', constraint.name)],
             )
 
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_opclass_func(self):
+        constraint = UniqueConstraint(
+            OpClass(Lower('scene'), name='text_pattern_ops'),
+            name='test_opclass_func',
+        )
+        with connection.schema_editor() as editor:
+            editor.add_constraint(Scene, constraint)
+        constraints = self.get_constraints(Scene._meta.db_table)
+        self.assertIs(constraints[constraint.name]['unique'], True)
+        self.assertIn(constraint.name, constraints)
+        with editor.connection.cursor() as cursor:
+            cursor.execute(self.get_opclass_query, [constraint.name])
+            self.assertEqual(
+                cursor.fetchall(),
+                [('text_pattern_ops', constraint.name)],
+            )
+        Scene.objects.create(scene='Scene 10', setting='The dark forest of Ewing')
+        with self.assertRaises(IntegrityError), transaction.atomic():
+            Scene.objects.create(scene='ScEnE 10', setting="Sir Bedemir's Castle")
+        Scene.objects.create(scene='Scene 5', setting="Sir Bedemir's Castle")
+        # Drop the constraint.
+        with connection.schema_editor() as editor:
+            editor.remove_constraint(Scene, constraint)
+        self.assertNotIn(constraint.name, self.get_constraints(Scene._meta.db_table))
+        Scene.objects.create(scene='ScEnE 10', setting="Sir Bedemir's Castle")
+
 
 class ExclusionConstraintTests(PostgreSQLTestCase):
     def get_constraints(self, table):
diff --git a/tests/schema/tests.py b/tests/schema/tests.py
index 4522f5faf4..fd8874e157 100644
--- a/tests/schema/tests.py
+++ b/tests/schema/tests.py
@@ -2189,6 +2189,246 @@ class SchemaTests(TransactionTestCase):
             AuthorWithUniqueNameAndBirthday._meta.constraints = []
             editor.remove_constraint(AuthorWithUniqueNameAndBirthday, constraint)
 
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint(self):
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+        constraint = UniqueConstraint(Upper('name').desc(), name='func_upper_uq')
+        # Add constraint.
+        with connection.schema_editor() as editor:
+            editor.add_constraint(Author, constraint)
+            sql = constraint.create_sql(Author, editor)
+        table = Author._meta.db_table
+        constraints = self.get_constraints(table)
+        if connection.features.supports_index_column_ordering:
+            self.assertIndexOrder(table, constraint.name, ['DESC'])
+        self.assertIn(constraint.name, constraints)
+        self.assertIs(constraints[constraint.name]['unique'], True)
+        # SQL contains a database function.
+        self.assertIs(sql.references_column(table, 'name'), True)
+        self.assertIn('UPPER(%s)' % editor.quote_name('name'), str(sql))
+        # Remove constraint.
+        with connection.schema_editor() as editor:
+            editor.remove_constraint(Author, constraint)
+        self.assertNotIn(constraint.name, self.get_constraints(table))
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_composite_func_unique_constraint(self):
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+            editor.create_model(BookWithSlug)
+        constraint = UniqueConstraint(
+            Upper('title'),
+            Lower('slug'),
+            name='func_upper_lower_unq',
+        )
+        # Add constraint.
+        with connection.schema_editor() as editor:
+            editor.add_constraint(BookWithSlug, constraint)
+            sql = constraint.create_sql(BookWithSlug, editor)
+        table = BookWithSlug._meta.db_table
+        constraints = self.get_constraints(table)
+        self.assertIn(constraint.name, constraints)
+        self.assertIs(constraints[constraint.name]['unique'], True)
+        # SQL contains database functions.
+        self.assertIs(sql.references_column(table, 'title'), True)
+        self.assertIs(sql.references_column(table, 'slug'), True)
+        sql = str(sql)
+        self.assertIn('UPPER(%s)' % editor.quote_name('title'), sql)
+        self.assertIn('LOWER(%s)' % editor.quote_name('slug'), sql)
+        self.assertLess(sql.index('UPPER'), sql.index('LOWER'))
+        # Remove constraint.
+        with connection.schema_editor() as editor:
+            editor.remove_constraint(BookWithSlug, constraint)
+        self.assertNotIn(constraint.name, self.get_constraints(table))
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_unique_constraint_field_and_expression(self):
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+        constraint = UniqueConstraint(
+            F('height').desc(),
+            'uuid',
+            Lower('name').asc(),
+            name='func_f_lower_field_unq',
+        )
+        # Add constraint.
+        with connection.schema_editor() as editor:
+            editor.add_constraint(Author, constraint)
+            sql = constraint.create_sql(Author, editor)
+        table = Author._meta.db_table
+        if connection.features.supports_index_column_ordering:
+            self.assertIndexOrder(table, constraint.name, ['DESC', 'ASC', 'ASC'])
+        constraints = self.get_constraints(table)
+        self.assertIs(constraints[constraint.name]['unique'], True)
+        self.assertEqual(len(constraints[constraint.name]['columns']), 3)
+        self.assertEqual(constraints[constraint.name]['columns'][1], 'uuid')
+        # SQL contains database functions and columns.
+        self.assertIs(sql.references_column(table, 'height'), True)
+        self.assertIs(sql.references_column(table, 'name'), True)
+        self.assertIs(sql.references_column(table, 'uuid'), True)
+        self.assertIn('LOWER(%s)' % editor.quote_name('name'), str(sql))
+        # Remove constraint.
+        with connection.schema_editor() as editor:
+            editor.remove_constraint(Author, constraint)
+        self.assertNotIn(constraint.name, self.get_constraints(table))
+
+    @skipUnlessDBFeature('supports_expression_indexes', 'supports_partial_indexes')
+    def test_func_unique_constraint_partial(self):
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+        constraint = UniqueConstraint(
+            Upper('name'),
+            name='func_upper_cond_weight_uq',
+            condition=Q(weight__isnull=False),
+        )
+        # Add constraint.
+        with connection.schema_editor() as editor:
+            editor.add_constraint(Author, constraint)
+            sql = constraint.create_sql(Author, editor)
+        table = Author._meta.db_table
+        constraints = self.get_constraints(table)
+        self.assertIn(constraint.name, constraints)
+        self.assertIs(constraints[constraint.name]['unique'], True)
+        self.assertIs(sql.references_column(table, 'name'), True)
+        self.assertIn('UPPER(%s)' % editor.quote_name('name'), str(sql))
+        self.assertIn(
+            'WHERE %s IS NOT NULL' % editor.quote_name('weight'),
+            str(sql),
+        )
+        # Remove constraint.
+        with connection.schema_editor() as editor:
+            editor.remove_constraint(Author, constraint)
+        self.assertNotIn(constraint.name, self.get_constraints(table))
+
+    @skipUnlessDBFeature('supports_expression_indexes', 'supports_covering_indexes')
+    def test_func_unique_constraint_covering(self):
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+        constraint = UniqueConstraint(
+            Upper('name'),
+            name='func_upper_covering_uq',
+            include=['weight', 'height'],
+        )
+        # Add constraint.
+        with connection.schema_editor() as editor:
+            editor.add_constraint(Author, constraint)
+            sql = constraint.create_sql(Author, editor)
+        table = Author._meta.db_table
+        constraints = self.get_constraints(table)
+        self.assertIn(constraint.name, constraints)
+        self.assertIs(constraints[constraint.name]['unique'], True)
+        self.assertEqual(
+            constraints[constraint.name]['columns'],
+            [None, 'weight', 'height'],
+        )
+        self.assertIs(sql.references_column(table, 'name'), True)
+        self.assertIs(sql.references_column(table, 'weight'), True)
+        self.assertIs(sql.references_column(table, 'height'), True)
+        self.assertIn('UPPER(%s)' % editor.quote_name('name'), str(sql))
+        self.assertIn(
+            'INCLUDE (%s, %s)' % (
+                editor.quote_name('weight'),
+                editor.quote_name('height'),
+            ),
+            str(sql),
+        )
+        # Remove constraint.
+        with connection.schema_editor() as editor:
+            editor.remove_constraint(Author, constraint)
+        self.assertNotIn(constraint.name, self.get_constraints(table))
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_lookups(self):
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+        with register_lookup(CharField, Lower), register_lookup(IntegerField, Abs):
+            constraint = UniqueConstraint(
+                F('name__lower'),
+                F('weight__abs'),
+                name='func_lower_abs_lookup_uq',
+            )
+            # Add constraint.
+            with connection.schema_editor() as editor:
+                editor.add_constraint(Author, constraint)
+                sql = constraint.create_sql(Author, editor)
+        table = Author._meta.db_table
+        constraints = self.get_constraints(table)
+        self.assertIn(constraint.name, constraints)
+        self.assertIs(constraints[constraint.name]['unique'], True)
+        # SQL contains columns.
+        self.assertIs(sql.references_column(table, 'name'), True)
+        self.assertIs(sql.references_column(table, 'weight'), True)
+        # Remove constraint.
+        with connection.schema_editor() as editor:
+            editor.remove_constraint(Author, constraint)
+        self.assertNotIn(constraint.name, self.get_constraints(table))
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_collate(self):
+        collation = connection.features.test_collations.get('non_default')
+        if not collation:
+            self.skipTest(
+                'This backend does not support case-insensitive collations.'
+            )
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+            editor.create_model(BookWithSlug)
+        constraint = UniqueConstraint(
+            Collate(F('title'), collation=collation).desc(),
+            Collate('slug', collation=collation),
+            name='func_collate_uq',
+        )
+        # Add constraint.
+        with connection.schema_editor() as editor:
+            editor.add_constraint(BookWithSlug, constraint)
+            sql = constraint.create_sql(BookWithSlug, editor)
+        table = BookWithSlug._meta.db_table
+        constraints = self.get_constraints(table)
+        self.assertIn(constraint.name, constraints)
+        self.assertIs(constraints[constraint.name]['unique'], True)
+        if connection.features.supports_index_column_ordering:
+            self.assertIndexOrder(table, constraint.name, ['DESC', 'ASC'])
+        # SQL contains columns and a collation.
+        self.assertIs(sql.references_column(table, 'title'), True)
+        self.assertIs(sql.references_column(table, 'slug'), True)
+        self.assertIn('COLLATE %s' % editor.quote_name(collation), str(sql))
+        # Remove constraint.
+        with connection.schema_editor() as editor:
+            editor.remove_constraint(BookWithSlug, constraint)
+        self.assertNotIn(constraint.name, self.get_constraints(table))
+
+    @skipIfDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_unsupported(self):
+        # UniqueConstraint is ignored on databases that don't support indexes on
+        # expressions.
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+        constraint = UniqueConstraint(F('name'), name='func_name_uq')
+        with connection.schema_editor() as editor, self.assertNumQueries(0):
+            self.assertIsNone(editor.add_constraint(Author, constraint))
+            self.assertIsNone(editor.remove_constraint(Author, constraint))
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_nonexistent_field(self):
+        constraint = UniqueConstraint(Lower('nonexistent'), name='func_nonexistent_uq')
+        msg = (
+            "Cannot resolve keyword 'nonexistent' into field. Choices are: "
+            "height, id, name, uuid, weight"
+        )
+        with self.assertRaisesMessage(FieldError, msg):
+            with connection.schema_editor() as editor:
+                editor.add_constraint(Author, constraint)
+
+    @skipUnlessDBFeature('supports_expression_indexes')
+    def test_func_unique_constraint_nondeterministic(self):
+        with connection.schema_editor() as editor:
+            editor.create_model(Author)
+        constraint = UniqueConstraint(Random(), name='func_random_uq')
+        with connection.schema_editor() as editor:
+            with self.assertRaises(DatabaseError):
+                editor.add_constraint(Author, constraint)
+
     def test_index_together(self):
         """
         Tests removing and adding index_together constraints on a model.