diff --git a/django/db/backends/base/schema.py b/django/db/backends/base/schema.py
index 578bfb244c..113d1b7f67 100644
--- a/django/db/backends/base/schema.py
+++ b/django/db/backends/base/schema.py
@@ -80,6 +80,7 @@ class BaseDatabaseSchemaEditor:
     sql_delete_fk = sql_delete_constraint
 
     sql_create_index = "CREATE INDEX %(name)s ON %(table)s (%(columns)s)%(extra)s%(condition)s"
+    sql_create_unique_index = "CREATE UNIQUE INDEX %(name)s ON %(table)s (%(columns)s)%(condition)s"
     sql_delete_index = "DROP INDEX %(name)s"
 
     sql_create_pk = "ALTER TABLE %(table)s ADD CONSTRAINT %(name)s PRIMARY KEY (%(columns)s)"
@@ -296,7 +297,7 @@ class BaseDatabaseSchemaEditor:
         # Make the table
         sql = self.sql_create_table % {
             "table": self.quote_name(model._meta.db_table),
-            "definition": ", ".join((*column_sqls, *constraints)),
+            "definition": ", ".join(constraint for constraint in (*column_sqls, *constraints) if constraint),
         }
         if model._meta.db_tablespace:
             tablespace_sql = self.connection.ops.tablespace_sql(model._meta.db_tablespace)
@@ -339,11 +340,15 @@ class BaseDatabaseSchemaEditor:
 
     def add_constraint(self, model, constraint):
         """Add a check constraint to a model."""
-        self.execute(constraint.create_sql(model, self))
+        sql = constraint.create_sql(model, self)
+        if sql:
+            self.execute(sql)
 
     def remove_constraint(self, model, constraint):
         """Remove a check constraint from a model."""
-        self.execute(constraint.remove_sql(model, self))
+        sql = constraint.remove_sql(model, self)
+        if sql:
+            self.execute(sql)
 
     def alter_unique_together(self, model, old_unique_together, new_unique_together):
         """
@@ -1008,7 +1013,14 @@ class BaseDatabaseSchemaEditor:
     def _delete_fk_sql(self, model, name):
         return self._delete_constraint_sql(self.sql_delete_fk, model, name)
 
-    def _unique_sql(self, fields, name):
+    def _unique_sql(self, model, fields, name, condition=None):
+        if condition:
+            # Databases support conditional unique constraints via a unique
+            # index.
+            sql = self._create_unique_sql(model, fields, name=name, condition=condition)
+            if sql:
+                self.deferred_sql.append(sql)
+            return None
         constraint = self.sql_unique_constraint % {
             'columns': ', '.join(map(self.quote_name, fields)),
         }
@@ -1017,7 +1029,7 @@ class BaseDatabaseSchemaEditor:
             'constraint': constraint,
         }
 
-    def _create_unique_sql(self, model, columns, name=None):
+    def _create_unique_sql(self, model, columns, name=None, condition=None):
         def create_unique_name(*args, **kwargs):
             return self.quote_name(self._create_index_name(*args, **kwargs))
 
@@ -1027,14 +1039,28 @@ class BaseDatabaseSchemaEditor:
         else:
             name = self.quote_name(name)
         columns = Columns(table, columns, self.quote_name)
-        return Statement(
-            self.sql_create_unique,
-            table=table,
-            name=name,
-            columns=columns,
-        )
+        if condition:
+            return Statement(
+                self.sql_create_unique_index,
+                table=table,
+                name=name,
+                columns=columns,
+                condition=' WHERE ' + condition,
+            ) if self.connection.features.supports_partial_indexes else None
+        else:
+            return Statement(
+                self.sql_create_unique,
+                table=table,
+                name=name,
+                columns=columns,
+            )
 
-    def _delete_unique_sql(self, model, name):
+    def _delete_unique_sql(self, model, name, condition=None):
+        if condition:
+            return (
+                self._delete_constraint_sql(self.sql_delete_index, model, name)
+                if self.connection.features.supports_partial_indexes else None
+            )
         return self._delete_constraint_sql(self.sql_delete_unique, model, name)
 
     def _check_sql(self, name, check):
diff --git a/django/db/backends/sqlite3/schema.py b/django/db/backends/sqlite3/schema.py
index e8e40bbe34..b1c91dba3c 100644
--- a/django/db/backends/sqlite3/schema.py
+++ b/django/db/backends/sqlite3/schema.py
@@ -4,6 +4,7 @@ from decimal import Decimal
 from django.apps.registry import Apps
 from django.db.backends.base.schema import BaseDatabaseSchemaEditor
 from django.db.backends.ddl_references import Statement
+from django.db.models import UniqueConstraint
 from django.db.transaction import atomic
 from django.db.utils import NotSupportedError
 
@@ -398,7 +399,13 @@ class DatabaseSchemaEditor(BaseDatabaseSchemaEditor):
         self.delete_model(old_field.remote_field.through)
 
     def add_constraint(self, model, constraint):
-        self._remake_table(model)
+        if isinstance(constraint, UniqueConstraint) and constraint.condition:
+            super().add_constraint(model, constraint)
+        else:
+            self._remake_table(model)
 
     def remove_constraint(self, model, constraint):
-        self._remake_table(model)
+        if isinstance(constraint, UniqueConstraint) and constraint.condition:
+            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 b55c5a32b1..faed79cc2f 100644
--- a/django/db/models/base.py
+++ b/django/db/models/base.py
@@ -1009,6 +1009,8 @@ class Model(metaclass=ModelBase):
         for model_class, model_constraints in constraints:
             for constraint in model_constraints:
                 if (isinstance(constraint, UniqueConstraint) and
+                        # Partial unique constraints can't be validated.
+                        constraint.condition is None and
                         not any(name in exclude for name in constraint.fields)):
                     unique_checks.append((model_class, constraint.fields))
 
diff --git a/django/db/models/constraints.py b/django/db/models/constraints.py
index 5b6f498d94..e7f81d3ee9 100644
--- a/django/db/models/constraints.py
+++ b/django/db/models/constraints.py
@@ -1,3 +1,4 @@
+from django.db.models.query_utils import Q
 from django.db.models.sql.query import Query
 
 __all__ = ['CheckConstraint', 'UniqueConstraint']
@@ -66,34 +67,55 @@ class CheckConstraint(BaseConstraint):
 
 
 class UniqueConstraint(BaseConstraint):
-    def __init__(self, *, fields, name):
+    def __init__(self, *, fields, name, condition=None):
         if not fields:
             raise ValueError('At least one field is required to define a unique constraint.')
+        if not isinstance(condition, (type(None), Q)):
+            raise ValueError('UniqueConstraint.condition must be a Q instance.')
         self.fields = tuple(fields)
+        self.condition = condition
         super().__init__(name)
 
+    def _get_condition_sql(self, model, schema_editor):
+        if self.condition is None:
+            return None
+        query = Query(model=model)
+        where = query.build_where(self.condition)
+        compiler = query.get_compiler(connection=schema_editor.connection)
+        sql, params = where.as_sql(compiler, schema_editor.connection)
+        return sql % tuple(schema_editor.quote_value(p) for p in params)
+
     def constraint_sql(self, model, schema_editor):
         fields = [model._meta.get_field(field_name).column for field_name in self.fields]
-        return schema_editor._unique_sql(fields, self.name)
+        condition = self._get_condition_sql(model, schema_editor)
+        return schema_editor._unique_sql(model, fields, self.name, condition=condition)
 
     def create_sql(self, model, schema_editor):
         fields = [model._meta.get_field(field_name).column for field_name in self.fields]
-        return schema_editor._create_unique_sql(model, fields, self.name)
+        condition = self._get_condition_sql(model, schema_editor)
+        return schema_editor._create_unique_sql(model, fields, self.name, condition=condition)
 
     def remove_sql(self, model, schema_editor):
-        return schema_editor._delete_unique_sql(model, self.name)
+        condition = self._get_condition_sql(model, schema_editor)
+        return schema_editor._delete_unique_sql(model, self.name, condition=condition)
 
     def __repr__(self):
-        return '<%s: fields=%r name=%r>' % (self.__class__.__name__, self.fields, self.name)
+        return '<%s: fields=%r name=%r%s>' % (
+            self.__class__.__name__, self.fields, self.name,
+            '' if self.condition is None else ' condition=%s' % self.condition,
+        )
 
     def __eq__(self, other):
         return (
             isinstance(other, UniqueConstraint) and
             self.name == other.name and
-            self.fields == other.fields
+            self.fields == other.fields and
+            self.condition == other.condition
         )
 
     def deconstruct(self):
         path, args, kwargs = super().deconstruct()
         kwargs['fields'] = self.fields
+        if self.condition:
+            kwargs['condition'] = self.condition
         return path, args, kwargs
diff --git a/docs/ref/models/constraints.txt b/docs/ref/models/constraints.txt
index c92d2dde37..acf3375b4a 100644
--- a/docs/ref/models/constraints.txt
+++ b/docs/ref/models/constraints.txt
@@ -69,3 +69,17 @@ date.
 .. attribute:: UniqueConstraint.name
 
 The name of the constraint.
+
+``condition``
+-------------
+
+.. attribute:: UniqueConstraint.condition
+
+A :class:`Q` object that specifies the condition you want the constraint to
+enforce.
+
+For example, ``UniqueConstraint(fields=['user'], condition=Q(status='DRAFT')``
+ensures that each user only has one draft.
+
+These conditions have the same database restrictions as
+:attr:`Index.condition`.
diff --git a/tests/constraints/models.py b/tests/constraints/models.py
index b1645ecedb..f316b95161 100644
--- a/tests/constraints/models.py
+++ b/tests/constraints/models.py
@@ -3,6 +3,7 @@ from django.db import models
 
 class Product(models.Model):
     name = models.CharField(max_length=255)
+    color = models.CharField(max_length=32, null=True)
     price = models.IntegerField(null=True)
     discounted_price = models.IntegerField(null=True)
 
@@ -12,5 +13,10 @@ class Product(models.Model):
                 check=models.Q(price__gt=models.F('discounted_price')),
                 name='price_gt_discounted_price',
             ),
-            models.UniqueConstraint(fields=['name'], name='unique_name'),
+            models.UniqueConstraint(fields=['name', 'color'], name='name_color_uniq'),
+            models.UniqueConstraint(
+                fields=['name'],
+                name='name_without_color_uniq',
+                condition=models.Q(color__isnull=True),
+            ),
         ]
diff --git a/tests/constraints/tests.py b/tests/constraints/tests.py
index 0e769ba321..b7aeb1e7f0 100644
--- a/tests/constraints/tests.py
+++ b/tests/constraints/tests.py
@@ -83,7 +83,10 @@ class CheckConstraintTests(TestCase):
 class UniqueConstraintTests(TestCase):
     @classmethod
     def setUpTestData(cls):
-        cls.p1 = Product.objects.create(name='p1')
+        cls.p1, cls.p2 = Product.objects.bulk_create([
+            Product(name='p1', color='red'),
+            Product(name='p2'),
+        ])
 
     def test_eq(self):
         self.assertEqual(
@@ -100,6 +103,29 @@ class UniqueConstraintTests(TestCase):
         )
         self.assertNotEqual(models.UniqueConstraint(fields=['foo', 'bar'], name='unique'), 1)
 
+    def test_eq_with_condition(self):
+        self.assertEqual(
+            models.UniqueConstraint(
+                fields=['foo', 'bar'], name='unique',
+                condition=models.Q(foo=models.F('bar'))
+            ),
+            models.UniqueConstraint(
+                fields=['foo', 'bar'], name='unique',
+                condition=models.Q(foo=models.F('bar'))),
+        )
+        self.assertNotEqual(
+            models.UniqueConstraint(
+                fields=['foo', 'bar'],
+                name='unique',
+                condition=models.Q(foo=models.F('bar'))
+            ),
+            models.UniqueConstraint(
+                fields=['foo', 'bar'],
+                name='unique',
+                condition=models.Q(foo=models.F('baz'))
+            ),
+        )
+
     def test_repr(self):
         fields = ['foo', 'bar']
         name = 'unique_fields'
@@ -109,6 +135,18 @@ class UniqueConstraintTests(TestCase):
             "<UniqueConstraint: fields=('foo', 'bar') name='unique_fields'>",
         )
 
+    def test_repr_with_condition(self):
+        constraint = models.UniqueConstraint(
+            fields=['foo', 'bar'],
+            name='unique_fields',
+            condition=models.Q(foo=models.F('bar')),
+        )
+        self.assertEqual(
+            repr(constraint),
+            "<UniqueConstraint: fields=('foo', 'bar') name='unique_fields' "
+            "condition=(AND: ('foo', F(bar)))>",
+        )
+
     def test_deconstruction(self):
         fields = ['foo', 'bar']
         name = 'unique_fields'
@@ -118,15 +156,34 @@ class UniqueConstraintTests(TestCase):
         self.assertEqual(args, ())
         self.assertEqual(kwargs, {'fields': tuple(fields), 'name': name})
 
+    def test_deconstruction_with_condition(self):
+        fields = ['foo', 'bar']
+        name = 'unique_fields'
+        condition = models.Q(foo=models.F('bar'))
+        constraint = models.UniqueConstraint(fields=fields, name=name, condition=condition)
+        path, args, kwargs = constraint.deconstruct()
+        self.assertEqual(path, 'django.db.models.UniqueConstraint')
+        self.assertEqual(args, ())
+        self.assertEqual(kwargs, {'fields': tuple(fields), 'name': name, 'condition': condition})
+
     def test_database_constraint(self):
         with self.assertRaises(IntegrityError):
-            Product.objects.create(name=self.p1.name)
+            Product.objects.create(name=self.p1.name, color=self.p1.color)
 
     def test_model_validation(self):
-        with self.assertRaisesMessage(ValidationError, 'Product with this Name already exists.'):
-            Product(name=self.p1.name).validate_unique()
+        with self.assertRaisesMessage(ValidationError, 'Product with this Name and Color already exists.'):
+            Product(name=self.p1.name, color=self.p1.color).validate_unique()
+
+    def test_model_validation_with_condition(self):
+        """Partial unique constraints are ignored by Model.validate_unique()."""
+        Product(name=self.p1.name, color='blue').validate_unique()
+        Product(name=self.p2.name).validate_unique()
 
     def test_name(self):
         constraints = get_constraints(Product._meta.db_table)
-        expected_name = 'unique_name'
+        expected_name = 'name_color_uniq'
         self.assertIn(expected_name, constraints)
+
+    def test_condition_must_be_q(self):
+        with self.assertRaisesMessage(ValueError, 'UniqueConstraint.condition must be a Q instance.'):
+            models.UniqueConstraint(name='uniq', fields=['name'], condition='invalid')
diff --git a/tests/migrations/test_operations.py b/tests/migrations/test_operations.py
index 2f35b5ba8f..e6d0c4bce4 100644
--- a/tests/migrations/test_operations.py
+++ b/tests/migrations/test_operations.py
@@ -501,6 +501,51 @@ class OperationTests(OperationTestBase):
         self.assertEqual(definition[1], [])
         self.assertEqual(definition[2]['options']['constraints'], [check_constraint])
 
+    def test_create_model_with_partial_unique_constraint(self):
+        partial_unique_constraint = models.UniqueConstraint(
+            fields=['pink'],
+            condition=models.Q(weight__gt=5),
+            name='test_constraint_pony_pink_for_weight_gt_5_uniq',
+        )
+        operation = migrations.CreateModel(
+            'Pony',
+            [
+                ('id', models.AutoField(primary_key=True)),
+                ('pink', models.IntegerField(default=3)),
+                ('weight', models.FloatField()),
+            ],
+            options={'constraints': [partial_unique_constraint]},
+        )
+        # Test the state alteration
+        project_state = ProjectState()
+        new_state = project_state.clone()
+        operation.state_forwards('test_crmo', new_state)
+        self.assertEqual(len(new_state.models['test_crmo', 'pony'].options['constraints']), 1)
+        # Test database alteration
+        self.assertTableNotExists('test_crmo_pony')
+        with connection.schema_editor() as editor:
+            operation.database_forwards('test_crmo', editor, project_state, new_state)
+        self.assertTableExists('test_crmo_pony')
+        # Test constraint works
+        Pony = new_state.apps.get_model('test_crmo', 'Pony')
+        Pony.objects.create(pink=1, weight=4.0)
+        Pony.objects.create(pink=1, weight=4.0)
+        Pony.objects.create(pink=1, weight=6.0)
+        if connection.features.supports_partial_indexes:
+            with self.assertRaises(IntegrityError):
+                Pony.objects.create(pink=1, weight=7.0)
+        else:
+            Pony.objects.create(pink=1, weight=7.0)
+        # Test reversal
+        with connection.schema_editor() as editor:
+            operation.database_backwards('test_crmo', editor, new_state, project_state)
+        self.assertTableNotExists('test_crmo_pony')
+        # Test deconstruction
+        definition = operation.deconstruct()
+        self.assertEqual(definition[0], 'CreateModel')
+        self.assertEqual(definition[1], [])
+        self.assertEqual(definition[2]['options']['constraints'], [partial_unique_constraint])
+
     def test_create_model_managers(self):
         """
         The managers on a model are set.
@@ -1854,6 +1899,92 @@ class OperationTests(OperationTestBase):
         self.assertEqual(definition[1], [])
         self.assertEqual(definition[2], {'model_name': "Pony", 'name': "test_remove_constraint_pony_pink_gt_2"})
 
+    def test_add_partial_unique_constraint(self):
+        project_state = self.set_up_test_model('test_addpartialuniqueconstraint')
+        partial_unique_constraint = models.UniqueConstraint(
+            fields=['pink'],
+            condition=models.Q(weight__gt=5),
+            name='test_constraint_pony_pink_for_weight_gt_5_uniq',
+        )
+        operation = migrations.AddConstraint('Pony', partial_unique_constraint)
+        self.assertEqual(
+            operation.describe(),
+            'Create constraint test_constraint_pony_pink_for_weight_gt_5_uniq '
+            'on model Pony'
+        )
+        # Test the state alteration
+        new_state = project_state.clone()
+        operation.state_forwards('test_addpartialuniqueconstraint', new_state)
+        self.assertEqual(len(new_state.models['test_addpartialuniqueconstraint', 'pony'].options['constraints']), 1)
+        Pony = new_state.apps.get_model('test_addpartialuniqueconstraint', 'Pony')
+        self.assertEqual(len(Pony._meta.constraints), 1)
+        # Test the database alteration
+        with connection.schema_editor() as editor:
+            operation.database_forwards('test_addpartialuniqueconstraint', editor, project_state, new_state)
+        # Test constraint works
+        Pony.objects.create(pink=1, weight=4.0)
+        Pony.objects.create(pink=1, weight=4.0)
+        Pony.objects.create(pink=1, weight=6.0)
+        if connection.features.supports_partial_indexes:
+            with self.assertRaises(IntegrityError), transaction.atomic():
+                Pony.objects.create(pink=1, weight=7.0)
+        else:
+            Pony.objects.create(pink=1, weight=7.0)
+        # Test reversal
+        with connection.schema_editor() as editor:
+            operation.database_backwards('test_addpartialuniqueconstraint', editor, new_state, project_state)
+        # Test constraint doesn't work
+        Pony.objects.create(pink=1, weight=7.0)
+        # Test deconstruction
+        definition = operation.deconstruct()
+        self.assertEqual(definition[0], 'AddConstraint')
+        self.assertEqual(definition[1], [])
+        self.assertEqual(definition[2], {'model_name': 'Pony', 'constraint': partial_unique_constraint})
+
+    def test_remove_partial_unique_constraint(self):
+        project_state = self.set_up_test_model('test_removepartialuniqueconstraint', constraints=[
+            models.UniqueConstraint(
+                fields=['pink'],
+                condition=models.Q(weight__gt=5),
+                name='test_constraint_pony_pink_for_weight_gt_5_uniq',
+            ),
+        ])
+        gt_operation = migrations.RemoveConstraint('Pony', 'test_constraint_pony_pink_for_weight_gt_5_uniq')
+        self.assertEqual(
+            gt_operation.describe(), 'Remove constraint test_constraint_pony_pink_for_weight_gt_5_uniq from model Pony'
+        )
+        # Test state alteration
+        new_state = project_state.clone()
+        gt_operation.state_forwards('test_removepartialuniqueconstraint', new_state)
+        self.assertEqual(len(new_state.models['test_removepartialuniqueconstraint', 'pony'].options['constraints']), 0)
+        Pony = new_state.apps.get_model('test_removepartialuniqueconstraint', 'Pony')
+        self.assertEqual(len(Pony._meta.constraints), 0)
+        # Test database alteration
+        with connection.schema_editor() as editor:
+            gt_operation.database_forwards('test_removepartialuniqueconstraint', editor, project_state, new_state)
+        # Test constraint doesn't work
+        Pony.objects.create(pink=1, weight=4.0)
+        Pony.objects.create(pink=1, weight=4.0)
+        Pony.objects.create(pink=1, weight=6.0)
+        Pony.objects.create(pink=1, weight=7.0).delete()
+        # Test reversal
+        with connection.schema_editor() as editor:
+            gt_operation.database_backwards('test_removepartialuniqueconstraint', editor, new_state, project_state)
+        # Test constraint works
+        if connection.features.supports_partial_indexes:
+            with self.assertRaises(IntegrityError), transaction.atomic():
+                Pony.objects.create(pink=1, weight=7.0)
+        else:
+            Pony.objects.create(pink=1, weight=7.0)
+        # Test deconstruction
+        definition = gt_operation.deconstruct()
+        self.assertEqual(definition[0], 'RemoveConstraint')
+        self.assertEqual(definition[1], [])
+        self.assertEqual(definition[2], {
+            'model_name': 'Pony',
+            'name': 'test_constraint_pony_pink_for_weight_gt_5_uniq',
+        })
+
     def test_alter_model_options(self):
         """
         Tests the AlterModelOptions operation.