diff --git a/django/db/backends/sqlite3/base.py b/django/db/backends/sqlite3/base.py
index 1fcc222c80b..f4fd1cc379a 100644
--- a/django/db/backends/sqlite3/base.py
+++ b/django/db/backends/sqlite3/base.py
@@ -18,6 +18,8 @@ from django.db.backends.signals import connection_created
 from django.db.backends.sqlite3.client import DatabaseClient
 from django.db.backends.sqlite3.creation import DatabaseCreation
 from django.db.backends.sqlite3.introspection import DatabaseIntrospection
+from django.db.models import fields
+from django.db.models.sql import aggregates
 from django.utils.dateparse import parse_date, parse_datetime, parse_time
 from django.utils.functional import cached_property
 from django.utils.safestring import SafeBytes
@@ -127,6 +129,17 @@ class DatabaseOperations(BaseDatabaseOperations):
         limit = 999 if len(fields) > 1 else 500
         return (limit // len(fields)) if len(fields) > 0 else len(objs)
 
+    def check_aggregate_support(self, aggregate):
+        bad_fields = (fields.DateField, fields.DateTimeField, fields.TimeField)
+        bad_aggregates = (aggregates.Sum, aggregates.Avg,
+                          aggregates.Variance, aggregates.StdDev)
+        if (isinstance(aggregate.source, bad_fields) and
+                isinstance(aggregate, bad_aggregates)):
+            raise NotImplementedError(
+                'You cannot use Sum, Avg, StdDev and Variance aggregations '
+                'on date/time fields in sqlite3 '
+                'since date/time is saved as text.')
+
     def date_extract_sql(self, lookup_type, field_name):
         # sqlite doesn't support extract, so we fake it with the user-defined
         # function django_extract that's registered in connect(). Note that
diff --git a/docs/ref/models/querysets.txt b/docs/ref/models/querysets.txt
index 2bbd895fd49..71049703c90 100644
--- a/docs/ref/models/querysets.txt
+++ b/docs/ref/models/querysets.txt
@@ -2188,6 +2188,14 @@ Django provides the following aggregation functions in the
 aggregate functions, see
 :doc:`the topic guide on aggregation </topics/db/aggregation>`.
 
+.. warning::
+
+    SQLite can't handle aggregation on date/time fields out of the box.
+    This is because there are no native date/time fields in SQLite and Django
+    currently emulates these features using a text field. Attempts to use
+    aggregation on date/time fields in SQLite will raise
+    ``NotImplementedError``.
+
 Avg
 ~~~
 
diff --git a/tests/regressiontests/backends/models.py b/tests/regressiontests/backends/models.py
index 344cf4c798d..a92aa71e174 100644
--- a/tests/regressiontests/backends/models.py
+++ b/tests/regressiontests/backends/models.py
@@ -75,3 +75,14 @@ class Article(models.Model):
 
     def __str__(self):
         return self.headline
+
+
+@python_2_unicode_compatible
+class Item(models.Model):
+    name = models.CharField(max_length=30)
+    date = models.DateField()
+    time = models.TimeField()
+    last_modified = models.DateTimeField()
+
+    def __str__(self):
+        return self.name
diff --git a/tests/regressiontests/backends/tests.py b/tests/regressiontests/backends/tests.py
index 791f4c1daa0..b29384739d8 100644
--- a/tests/regressiontests/backends/tests.py
+++ b/tests/regressiontests/backends/tests.py
@@ -12,6 +12,7 @@ from django.db import (backend, connection, connections, DEFAULT_DB_ALIAS,
     IntegrityError, transaction)
 from django.db.backends.signals import connection_created
 from django.db.backends.postgresql_psycopg2 import version as pg_version
+from django.db.models import fields, Sum, Avg, Variance, StdDev
 from django.db.utils import ConnectionHandler, DatabaseError, load_backend
 from django.test import (TestCase, skipUnlessDBFeature, skipIfDBFeature,
     TransactionTestCase)
@@ -362,6 +363,22 @@ class EscapingChecks(TestCase):
         self.assertTrue(int(response))
 
 
+class SqlliteAggregationTests(TestCase):
+    """
+    #19360: Raise NotImplementedError when aggregating on date/time fields.
+    """
+    @unittest.skipUnless(connection.vendor == 'sqlite',
+                         "No need to check SQLite aggregation semantics")
+    def test_aggregation(self):
+        for aggregate in (Sum, Avg, Variance, StdDev):
+            self.assertRaises(NotImplementedError,
+                models.Item.objects.all().aggregate, aggregate('time'))
+            self.assertRaises(NotImplementedError,
+                models.Item.objects.all().aggregate, aggregate('date'))
+            self.assertRaises(NotImplementedError,
+                models.Item.objects.all().aggregate, aggregate('last_modified'))
+
+
 class BackendTestCase(TestCase):
 
     def create_squares_with_executemany(self, args):
@@ -400,7 +417,6 @@ class BackendTestCase(TestCase):
             self.create_squares_with_executemany(args)
         self.assertEqual(models.Square.objects.count(), 9)
 
-
     def test_unicode_fetches(self):
         #6254: fetchone, fetchmany, fetchall return strings as unicode objects
         qn = connection.ops.quote_name