diff --git a/django/core/files/storage.py b/django/core/files/storage.py
index 16f9d4e27b..3e68853b59 100644
--- a/django/core/files/storage.py
+++ b/django/core/files/storage.py
@@ -1,4 +1,5 @@
 import os
+import pathlib
 from datetime import datetime
 from urllib.parse import urljoin
 
@@ -6,6 +7,7 @@ from django.conf import settings
 from django.core.exceptions import SuspiciousFileOperation
 from django.core.files import File, locks
 from django.core.files.move import file_move_safe
+from django.core.files.utils import validate_file_name
 from django.core.signals import setting_changed
 from django.utils import timezone
 from django.utils._os import safe_join
@@ -74,6 +76,9 @@ class Storage:
         available for new content to be written to.
         """
         dir_name, file_name = os.path.split(name)
+        if '..' in pathlib.PurePath(dir_name).parts:
+            raise SuspiciousFileOperation("Detected path traversal attempt in '%s'" % dir_name)
+        validate_file_name(file_name)
         file_root, file_ext = os.path.splitext(file_name)
         # If the filename already exists, generate an alternative filename
         # until it doesn't exist.
@@ -105,6 +110,8 @@ class Storage:
         """
         # `filename` may include a path as returned by FileField.upload_to.
         dirname, filename = os.path.split(filename)
+        if '..' in pathlib.PurePath(dirname).parts:
+            raise SuspiciousFileOperation("Detected path traversal attempt in '%s'" % dirname)
         return os.path.normpath(os.path.join(dirname, self.get_valid_name(filename)))
 
     def path(self, name):
diff --git a/django/core/files/uploadedfile.py b/django/core/files/uploadedfile.py
index 48007b8682..f452bcd9a4 100644
--- a/django/core/files/uploadedfile.py
+++ b/django/core/files/uploadedfile.py
@@ -8,6 +8,7 @@ from io import BytesIO
 from django.conf import settings
 from django.core.files import temp as tempfile
 from django.core.files.base import File
+from django.core.files.utils import validate_file_name
 
 __all__ = ('UploadedFile', 'TemporaryUploadedFile', 'InMemoryUploadedFile',
            'SimpleUploadedFile')
@@ -47,6 +48,8 @@ class UploadedFile(File):
                 ext = ext[:255]
                 name = name[:255 - len(ext)] + ext
 
+            name = validate_file_name(name)
+
         self._name = name
 
     name = property(_get_name, _set_name)
diff --git a/django/core/files/utils.py b/django/core/files/utils.py
index de89607175..f83cb1a3cf 100644
--- a/django/core/files/utils.py
+++ b/django/core/files/utils.py
@@ -1,3 +1,19 @@
+import os
+
+from django.core.exceptions import SuspiciousFileOperation
+
+
+def validate_file_name(name):
+    if name != os.path.basename(name):
+        raise SuspiciousFileOperation("File name '%s' includes path elements" % name)
+
+    # Remove potentially dangerous names
+    if name in {'', '.', '..'}:
+        raise SuspiciousFileOperation("Could not derive file name from '%s'" % name)
+
+    return name
+
+
 class FileProxyMixin:
     """
     A mixin class used to forward file methods to an underlaying file
diff --git a/django/db/models/fields/files.py b/django/db/models/fields/files.py
index d410771cf3..a2f972489f 100644
--- a/django/db/models/fields/files.py
+++ b/django/db/models/fields/files.py
@@ -6,6 +6,7 @@ from django.core import checks
 from django.core.files.base import File
 from django.core.files.images import ImageFile
 from django.core.files.storage import Storage, default_storage
+from django.core.files.utils import validate_file_name
 from django.db.models import signals
 from django.db.models.fields import Field
 from django.db.models.query_utils import DeferredAttribute
@@ -312,6 +313,7 @@ class FileField(Field):
         Until the storage layer, all file paths are expected to be Unix style
         (with forward slashes).
         """
+        filename = validate_file_name(filename)
         if callable(self.upload_to):
             filename = self.upload_to(instance, filename)
         else:
diff --git a/django/http/multipartparser.py b/django/http/multipartparser.py
index 180a533bb6..f464caa1b4 100644
--- a/django/http/multipartparser.py
+++ b/django/http/multipartparser.py
@@ -9,7 +9,6 @@ import binascii
 import cgi
 import collections
 import html
-import os
 from urllib.parse import unquote
 
 from django.conf import settings
@@ -306,10 +305,25 @@ class MultiPartParser:
                 break
 
     def sanitize_file_name(self, file_name):
+        """
+        Sanitize the filename of an upload.
+
+        Remove all possible path separators, even though that might remove more
+        than actually required by the target system. Filenames that could
+        potentially cause problems (current/parent dir) are also discarded.
+
+        It should be noted that this function could still return a "filepath"
+        like "C:some_file.txt" which is handled later on by the storage layer.
+        So while this function does sanitize filenames to some extent, the
+        resulting filename should still be considered as untrusted user input.
+        """
         file_name = html.unescape(file_name)
-        # Cleanup Windows-style path separators.
-        file_name = file_name[file_name.rfind('\\') + 1:].strip()
-        return os.path.basename(file_name)
+        file_name = file_name.rsplit('/')[-1]
+        file_name = file_name.rsplit('\\')[-1]
+
+        if file_name in {'', '.', '..'}:
+            return None
+        return file_name
 
     IE_sanitize = sanitize_file_name
 
diff --git a/django/utils/text.py b/django/utils/text.py
index 4d77ce7f41..baa44f279e 100644
--- a/django/utils/text.py
+++ b/django/utils/text.py
@@ -5,6 +5,7 @@ import warnings
 from gzip import GzipFile
 from io import BytesIO
 
+from django.core.exceptions import SuspiciousFileOperation
 from django.utils.deprecation import RemovedInDjango40Warning
 from django.utils.functional import SimpleLazyObject, keep_lazy_text, lazy
 from django.utils.regex_helper import _lazy_re_compile
@@ -219,7 +220,7 @@ class Truncator(SimpleLazyObject):
 
 
 @keep_lazy_text
-def get_valid_filename(s):
+def get_valid_filename(name):
     """
     Return the given string converted to a string that can be used for a clean
     filename. Remove leading and trailing spaces; convert other spaces to
@@ -228,8 +229,11 @@ def get_valid_filename(s):
     >>> get_valid_filename("john's portrait in 2004.jpg")
     'johns_portrait_in_2004.jpg'
     """
-    s = str(s).strip().replace(' ', '_')
-    return re.sub(r'(?u)[^-\w.]', '', s)
+    s = str(name).strip().replace(' ', '_')
+    s = re.sub(r'(?u)[^-\w.]', '', s)
+    if s in {'', '.', '..'}:
+        raise SuspiciousFileOperation("Could not derive file name from '%s'" % name)
+    return s
 
 
 @keep_lazy_text
diff --git a/docs/releases/2.2.21.txt b/docs/releases/2.2.21.txt
new file mode 100644
index 0000000000..f32aeadff7
--- /dev/null
+++ b/docs/releases/2.2.21.txt
@@ -0,0 +1,17 @@
+===========================
+Django 2.2.21 release notes
+===========================
+
+*May 4, 2021*
+
+Django 2.2.21 fixes a security issue in 2.2.20.
+
+CVE-2021-31542: Potential directory-traversal via uploaded files
+================================================================
+
+``MultiPartParser``, ``UploadedFile``, and ``FieldFile`` allowed
+directory-traversal via uploaded files with suitably crafted file names.
+
+In order to mitigate this risk, stricter basename and path sanitation is now
+applied. Specifically, empty file names and paths with dot segments will be
+rejected.
diff --git a/docs/releases/3.1.9.txt b/docs/releases/3.1.9.txt
new file mode 100644
index 0000000000..682270b901
--- /dev/null
+++ b/docs/releases/3.1.9.txt
@@ -0,0 +1,17 @@
+==========================
+Django 3.1.9 release notes
+==========================
+
+*May 4, 2021*
+
+Django 3.1.9 fixes a security issue in 3.1.8.
+
+CVE-2021-31542: Potential directory-traversal via uploaded files
+================================================================
+
+``MultiPartParser``, ``UploadedFile``, and ``FieldFile`` allowed
+directory-traversal via uploaded files with suitably crafted file names.
+
+In order to mitigate this risk, stricter basename and path sanitation is now
+applied. Specifically, empty file names and paths with dot segments will be
+rejected.
diff --git a/docs/releases/3.2.1.txt b/docs/releases/3.2.1.txt
index 545c9adce3..97ac4ebc94 100644
--- a/docs/releases/3.2.1.txt
+++ b/docs/releases/3.2.1.txt
@@ -2,9 +2,19 @@
 Django 3.2.1 release notes
 ==========================
 
-*Expected May 4, 2021*
+*May 4, 2021*
 
-Django 3.2.1 fixes several bugs in 3.2.
+Django 3.2.1 fixes a security issue and several bugs in 3.2.
+
+CVE-2021-31542: Potential directory-traversal via uploaded files
+================================================================
+
+``MultiPartParser``, ``UploadedFile``, and ``FieldFile`` allowed
+directory-traversal via uploaded files with suitably crafted file names.
+
+In order to mitigate this risk, stricter basename and path sanitation is now
+applied. Specifically, empty file names and paths with dot segments will be
+rejected.
 
 Bugfixes
 ========
diff --git a/docs/releases/index.txt b/docs/releases/index.txt
index ca1d1ed8ea..ea53ca0063 100644
--- a/docs/releases/index.txt
+++ b/docs/releases/index.txt
@@ -33,6 +33,7 @@ versions of the documentation contain the release notes for any later releases.
 .. toctree::
    :maxdepth: 1
 
+   3.1.9
    3.1.8
    3.1.7
    3.1.6
@@ -69,6 +70,7 @@ versions of the documentation contain the release notes for any later releases.
 .. toctree::
    :maxdepth: 1
 
+   2.2.21
    2.2.20
    2.2.19
    2.2.18
diff --git a/tests/file_storage/test_generate_filename.py b/tests/file_storage/test_generate_filename.py
index b4222f4121..9f54f6921e 100644
--- a/tests/file_storage/test_generate_filename.py
+++ b/tests/file_storage/test_generate_filename.py
@@ -1,7 +1,8 @@
 import os
 
+from django.core.exceptions import SuspiciousFileOperation
 from django.core.files.base import ContentFile
-from django.core.files.storage import Storage
+from django.core.files.storage import FileSystemStorage, Storage
 from django.db.models import FileField
 from django.test import SimpleTestCase
 
@@ -36,6 +37,44 @@ class AWSS3Storage(Storage):
 
 
 class GenerateFilenameStorageTests(SimpleTestCase):
+    def test_storage_dangerous_paths(self):
+        candidates = [
+            ('/tmp/..', '..'),
+            ('/tmp/.', '.'),
+            ('', ''),
+        ]
+        s = FileSystemStorage()
+        msg = "Could not derive file name from '%s'"
+        for file_name, base_name in candidates:
+            with self.subTest(file_name=file_name):
+                with self.assertRaisesMessage(SuspiciousFileOperation, msg % base_name):
+                    s.get_available_name(file_name)
+                with self.assertRaisesMessage(SuspiciousFileOperation, msg % base_name):
+                    s.generate_filename(file_name)
+
+    def test_storage_dangerous_paths_dir_name(self):
+        file_name = '/tmp/../path'
+        s = FileSystemStorage()
+        msg = "Detected path traversal attempt in '/tmp/..'"
+        with self.assertRaisesMessage(SuspiciousFileOperation, msg):
+            s.get_available_name(file_name)
+        with self.assertRaisesMessage(SuspiciousFileOperation, msg):
+            s.generate_filename(file_name)
+
+    def test_filefield_dangerous_filename(self):
+        candidates = ['..', '.', '', '???', '$.$.$']
+        f = FileField(upload_to='some/folder/')
+        msg = "Could not derive file name from '%s'"
+        for file_name in candidates:
+            with self.subTest(file_name=file_name):
+                with self.assertRaisesMessage(SuspiciousFileOperation, msg % file_name):
+                    f.generate_filename(None, file_name)
+
+    def test_filefield_dangerous_filename_dir(self):
+        f = FileField(upload_to='some/folder/')
+        msg = "File name '/tmp/path' includes path elements"
+        with self.assertRaisesMessage(SuspiciousFileOperation, msg):
+            f.generate_filename(None, '/tmp/path')
 
     def test_filefield_generate_filename(self):
         f = FileField(upload_to='some/folder/')
diff --git a/tests/file_uploads/tests.py b/tests/file_uploads/tests.py
index e8f91e2fa0..7bc8d41dac 100644
--- a/tests/file_uploads/tests.py
+++ b/tests/file_uploads/tests.py
@@ -9,8 +9,9 @@ from io import BytesIO, StringIO
 from unittest import mock
 from urllib.parse import quote
 
+from django.core.exceptions import SuspiciousFileOperation
 from django.core.files import temp as tempfile
-from django.core.files.uploadedfile import SimpleUploadedFile
+from django.core.files.uploadedfile import SimpleUploadedFile, UploadedFile
 from django.http.multipartparser import (
     FILE, MultiPartParser, MultiPartParserError, Parser, parse_header,
 )
@@ -39,6 +40,16 @@ CANDIDATE_TRAVERSAL_FILE_NAMES = [
     '../hax0rd.txt',        # HTML entities.
 ]
 
+CANDIDATE_INVALID_FILE_NAMES = [
+    '/tmp/',        # Directory, *nix-style.
+    'c:\\tmp\\',    # Directory, win-style.
+    '/tmp/.',       # Directory dot, *nix-style.
+    'c:\\tmp\\.',   # Directory dot, *nix-style.
+    '/tmp/..',      # Parent directory, *nix-style.
+    'c:\\tmp\\..',  # Parent directory, win-style.
+    '',             # Empty filename.
+]
+
 
 @override_settings(MEDIA_ROOT=MEDIA_ROOT, ROOT_URLCONF='file_uploads.urls', MIDDLEWARE=[])
 class FileUploadTests(TestCase):
@@ -53,6 +64,22 @@ class FileUploadTests(TestCase):
         shutil.rmtree(MEDIA_ROOT)
         super().tearDownClass()
 
+    def test_upload_name_is_validated(self):
+        candidates = [
+            '/tmp/',
+            '/tmp/..',
+            '/tmp/.',
+        ]
+        if sys.platform == 'win32':
+            candidates.extend([
+                'c:\\tmp\\',
+                'c:\\tmp\\..',
+                'c:\\tmp\\.',
+            ])
+        for file_name in candidates:
+            with self.subTest(file_name=file_name):
+                self.assertRaises(SuspiciousFileOperation, UploadedFile, name=file_name)
+
     def test_simple_upload(self):
         with open(__file__, 'rb') as fp:
             post_data = {
@@ -718,6 +745,15 @@ class MultiParserTests(SimpleTestCase):
             with self.subTest(file_name=file_name):
                 self.assertEqual(parser.sanitize_file_name(file_name), 'hax0rd.txt')
 
+    def test_sanitize_invalid_file_name(self):
+        parser = MultiPartParser({
+            'CONTENT_TYPE': 'multipart/form-data; boundary=_foo',
+            'CONTENT_LENGTH': '1',
+        }, StringIO('x'), [], 'utf-8')
+        for file_name in CANDIDATE_INVALID_FILE_NAMES:
+            with self.subTest(file_name=file_name):
+                self.assertIsNone(parser.sanitize_file_name(file_name))
+
     def test_rfc2231_parsing(self):
         test_data = (
             (b"Content-Type: application/x-stuff; title*=us-ascii'en-us'This%20is%20%2A%2A%2Afun%2A%2A%2A",
diff --git a/tests/forms_tests/field_tests/test_filefield.py b/tests/forms_tests/field_tests/test_filefield.py
index 261d9f4ca9..2db106e4a0 100644
--- a/tests/forms_tests/field_tests/test_filefield.py
+++ b/tests/forms_tests/field_tests/test_filefield.py
@@ -21,10 +21,12 @@ class FileFieldTest(SimpleTestCase):
             f.clean(None, '')
         self.assertEqual('files/test2.pdf', f.clean(None, 'files/test2.pdf'))
         no_file_msg = "'No file was submitted. Check the encoding type on the form.'"
+        file = SimpleUploadedFile(None, b'')
+        file._name = ''
         with self.assertRaisesMessage(ValidationError, no_file_msg):
-            f.clean(SimpleUploadedFile('', b''))
+            f.clean(file)
         with self.assertRaisesMessage(ValidationError, no_file_msg):
-            f.clean(SimpleUploadedFile('', b''), '')
+            f.clean(file, '')
         self.assertEqual('files/test3.pdf', f.clean(None, 'files/test3.pdf'))
         with self.assertRaisesMessage(ValidationError, no_file_msg):
             f.clean('some content that is not a file')
diff --git a/tests/utils_tests/test_text.py b/tests/utils_tests/test_text.py
index 1b6bfc0b8e..d2a94fcdab 100644
--- a/tests/utils_tests/test_text.py
+++ b/tests/utils_tests/test_text.py
@@ -1,6 +1,7 @@
 import json
 import sys
 
+from django.core.exceptions import SuspiciousFileOperation
 from django.test import SimpleTestCase, ignore_warnings
 from django.utils import text
 from django.utils.deprecation import RemovedInDjango40Warning
@@ -255,6 +256,13 @@ class TestUtilsText(SimpleTestCase):
         filename = "^&'@{}[],$=!-#()%+~_123.txt"
         self.assertEqual(text.get_valid_filename(filename), "-_123.txt")
         self.assertEqual(text.get_valid_filename(lazystr(filename)), "-_123.txt")
+        msg = "Could not derive file name from '???'"
+        with self.assertRaisesMessage(SuspiciousFileOperation, msg):
+            text.get_valid_filename('???')
+        # After sanitizing this would yield '..'.
+        msg = "Could not derive file name from '$.$.$'"
+        with self.assertRaisesMessage(SuspiciousFileOperation, msg):
+            text.get_valid_filename('$.$.$')
 
     def test_compress_sequence(self):
         data = [{'key': i} for i in range(10)]