diff --git a/django/db/models/query.py b/django/db/models/query.py
index b71e9a87d5..38f69f22d1 100644
--- a/django/db/models/query.py
+++ b/django/db/models/query.py
@@ -323,6 +323,7 @@ class QuerySet:
         """
         if self.query.distinct_fields:
             raise NotImplementedError("aggregate() + distinct(fields) not implemented.")
+        self._validate_values_are_expressions(args + tuple(kwargs.values()), method_name='aggregate')
         for arg in args:
             # The default_alias property raises TypeError if default_alias
             # can't be set automatically or AttributeError if it isn't an
@@ -895,6 +896,7 @@ class QuerySet:
         Return a query set in which the returned objects have been annotated
         with extra data or aggregations.
         """
+        self._validate_values_are_expressions(args + tuple(kwargs.values()), method_name='annotate')
         annotations = OrderedDict()  # To preserve ordering of args
         for arg in args:
             # The default_alias property may raise a TypeError.
@@ -1145,6 +1147,17 @@ class QuerySet:
         """
         return self.query.has_filters()
 
+    @staticmethod
+    def _validate_values_are_expressions(values, method_name):
+        invalid_args = sorted(str(arg) for arg in values if not hasattr(arg, 'resolve_expression'))
+        if invalid_args:
+            raise TypeError(
+                'QuerySet.%s() received non-expression(s): %s.' % (
+                    method_name,
+                    ', '.join(invalid_args),
+                )
+            )
+
 
 class InstanceCheckMeta(type):
     def __instancecheck__(self, instance):
diff --git a/tests/aggregation/tests.py b/tests/aggregation/tests.py
index 8cf0596347..c3f7998f60 100644
--- a/tests/aggregation/tests.py
+++ b/tests/aggregation/tests.py
@@ -1186,3 +1186,12 @@ class AggregateTestCase(TestCase):
         ).filter(rating_or_num_awards__gt=F('num_awards')).order_by('num_awards')
         self.assertQuerysetEqual(
             qs2, [1, 3], lambda v: v.num_awards)
+
+    def test_arguments_must_be_expressions(self):
+        msg = 'QuerySet.aggregate() received non-expression(s): %s.'
+        with self.assertRaisesMessage(TypeError, msg % FloatField()):
+            Book.objects.aggregate(FloatField())
+        with self.assertRaisesMessage(TypeError, msg % True):
+            Book.objects.aggregate(is_book=True)
+        with self.assertRaisesMessage(TypeError, msg % ', '.join([str(FloatField()), 'True'])):
+            Book.objects.aggregate(FloatField(), Avg('price'), is_book=True)
diff --git a/tests/annotations/tests.py b/tests/annotations/tests.py
index 981e73e43e..1714076e1d 100644
--- a/tests/annotations/tests.py
+++ b/tests/annotations/tests.py
@@ -508,3 +508,12 @@ class NonAggregateAnnotationTestCase(TestCase):
             self.assertIs(book.is_book, True)
             self.assertIs(book.is_pony, False)
             self.assertIsNone(book.is_none)
+
+    def test_arguments_must_be_expressions(self):
+        msg = 'QuerySet.annotate() received non-expression(s): %s.'
+        with self.assertRaisesMessage(TypeError, msg % BooleanField()):
+            Book.objects.annotate(BooleanField())
+        with self.assertRaisesMessage(TypeError, msg % True):
+            Book.objects.annotate(is_book=True)
+        with self.assertRaisesMessage(TypeError, msg % ', '.join([str(BooleanField()), 'True'])):
+            Book.objects.annotate(BooleanField(), Value(False), is_book=True)