diff --git a/django/core/checks/messages.py b/django/core/checks/messages.py
index aacac632eb4..0987c2d1188 100644
--- a/django/core/checks/messages.py
+++ b/django/core/checks/messages.py
@@ -9,7 +9,8 @@ CRITICAL = 50
 class CheckMessage:
 
     def __init__(self, level, msg, hint=None, obj=None, id=None):
-        assert isinstance(level, int), "The first argument should be level."
+        if not isinstance(level, int):
+            raise TypeError('The first argument should be level.')
         self.level = level
         self.msg = msg
         self.hint = hint
diff --git a/django/core/checks/registry.py b/django/core/checks/registry.py
index d54538e3673..d7bfa495486 100644
--- a/django/core/checks/registry.py
+++ b/django/core/checks/registry.py
@@ -75,9 +75,12 @@ class CheckRegistry:
 
         for check in checks:
             new_errors = check(app_configs=app_configs, databases=databases)
-            assert is_iterable(new_errors), (
-                "The function %r did not return a list. All functions registered "
-                "with the checks registry must return a list." % check)
+            if not is_iterable(new_errors):
+                raise TypeError(
+                    'The function %r did not return a list. All functions '
+                    'registered with the checks registry must return a list.'
+                    % check,
+                )
             errors.extend(new_errors)
         return errors
 
diff --git a/django/core/files/storage.py b/django/core/files/storage.py
index 16f9d4e27b1..29b0e4c9ed6 100644
--- a/django/core/files/storage.py
+++ b/django/core/files/storage.py
@@ -294,7 +294,8 @@ class FileSystemStorage(Storage):
         return str(name).replace('\\', '/')
 
     def delete(self, name):
-        assert name, "The name argument is not allowed to be empty."
+        if not name:
+            raise ValueError('The name must be given to delete().')
         name = self.path(name)
         # If the file or directory exists, delete it from the filesystem.
         try:
diff --git a/django/core/mail/message.py b/django/core/mail/message.py
index 963542cd623..ccc8a769ea3 100644
--- a/django/core/mail/message.py
+++ b/django/core/mail/message.py
@@ -296,11 +296,15 @@ class EmailMessage:
         mimetype to DEFAULT_ATTACHMENT_MIME_TYPE and don't decode the content.
         """
         if isinstance(filename, MIMEBase):
-            assert content is None
-            assert mimetype is None
+            if content is not None or mimetype is not None:
+                raise ValueError(
+                    'content and mimetype must not be given when a MIMEBase '
+                    'instance is provided.'
+                )
             self.attachments.append(filename)
+        elif content is None:
+            raise ValueError('content must be provided.')
         else:
-            assert content is not None
             mimetype = mimetype or mimetypes.guess_type(filename)[0] or DEFAULT_ATTACHMENT_MIME_TYPE
             basetype, subtype = mimetype.split('/', 1)
 
@@ -428,8 +432,8 @@ class EmailMultiAlternatives(EmailMessage):
 
     def attach_alternative(self, content, mimetype):
         """Attach an alternative content representation."""
-        assert content is not None
-        assert mimetype is not None
+        if content is None or mimetype is None:
+            raise ValueError('Both content and mimetype must be provided.')
         self.alternatives.append((content, mimetype))
 
     def _create_message(self, msg):
diff --git a/docs/releases/4.0.txt b/docs/releases/4.0.txt
index 56197115c6a..6f10124c0c5 100644
--- a/docs/releases/4.0.txt
+++ b/docs/releases/4.0.txt
@@ -355,6 +355,13 @@ Miscellaneous
   to ``reorder_tests()``. It now accepts an iterable of tests rather than a
   test suite, and returns an iterator of tests.
 
+* Calling ``FileSystemStorage.delete()`` with an empty ``name`` now raises
+  ``ValueError`` instead of ``AssertionError``.
+
+* Calling ``EmailMultiAlternatives.attach_alternative()`` or
+  ``EmailMessage.attach()`` with an invalid ``content`` or ``mimetype``
+  arguments now raise ``ValueError`` instead of ``AssertionError``.
+
 .. _deprecated-features-4.0:
 
 Features deprecated in 4.0
diff --git a/tests/check_framework/tests.py b/tests/check_framework/tests.py
index e669b11c2b8..9e461c5040a 100644
--- a/tests/check_framework/tests.py
+++ b/tests/check_framework/tests.py
@@ -4,6 +4,7 @@ from io import StringIO
 from django.apps import apps
 from django.core import checks
 from django.core.checks import Error, Warning
+from django.core.checks.messages import CheckMessage
 from django.core.checks.registry import CheckRegistry
 from django.core.management import call_command
 from django.core.management.base import CommandError
@@ -74,6 +75,20 @@ class SystemCheckFrameworkTests(SimpleTestCase):
             def no_kwargs(app_configs, databases):
                 pass
 
+    def test_register_run_checks_non_iterable(self):
+        registry = CheckRegistry()
+
+        @registry.register
+        def return_non_iterable(**kwargs):
+            return Error('Message')
+
+        msg = (
+            'The function %r did not return a list. All functions registered '
+            'with the checks registry must return a list.' % return_non_iterable
+        )
+        with self.assertRaisesMessage(TypeError, msg):
+            registry.run_checks()
+
 
 class MessageTests(SimpleTestCase):
 
@@ -132,6 +147,11 @@ class MessageTests(SimpleTestCase):
         e = Error("Error", obj=DummyObj())
         self.assertNotEqual(e, 'a string')
 
+    def test_invalid_level(self):
+        msg = 'The first argument should be level.'
+        with self.assertRaisesMessage(TypeError, msg):
+            CheckMessage('ERROR', 'Message')
+
 
 def simple_system_check(**kwargs):
     simple_system_check.kwargs = kwargs
diff --git a/tests/file_storage/tests.py b/tests/file_storage/tests.py
index 6d17a7118b4..381bc6b7b5c 100644
--- a/tests/file_storage/tests.py
+++ b/tests/file_storage/tests.py
@@ -501,7 +501,10 @@ class FileStorageTests(SimpleTestCase):
         Calling delete with an empty name should not try to remove the base
         storage directory, but fail loudly (#20660).
         """
-        with self.assertRaises(AssertionError):
+        msg = 'The name must be given to delete().'
+        with self.assertRaisesMessage(ValueError, msg):
+            self.storage.delete(None)
+        with self.assertRaisesMessage(ValueError, msg):
             self.storage.delete('')
 
     def test_delete_deletes_directories(self):
diff --git a/tests/mail/tests.py b/tests/mail/tests.py
index 475e204b32b..de8ff159c00 100644
--- a/tests/mail/tests.py
+++ b/tests/mail/tests.py
@@ -529,6 +529,24 @@ class MailTests(HeadersCheckMixin, SimpleTestCase):
         self.assertEqual(content, b'\xff')
         self.assertEqual(mimetype, 'application/octet-stream')
 
+    def test_attach_mimetext_content_mimetype(self):
+        email_msg = EmailMessage()
+        txt = MIMEText('content')
+        msg = (
+            'content and mimetype must not be given when a MIMEBase instance '
+            'is provided.'
+        )
+        with self.assertRaisesMessage(ValueError, msg):
+            email_msg.attach(txt, content='content')
+        with self.assertRaisesMessage(ValueError, msg):
+            email_msg.attach(txt, mimetype='text/plain')
+
+    def test_attach_content_none(self):
+        email_msg = EmailMessage()
+        msg = 'content must be provided.'
+        with self.assertRaisesMessage(ValueError, msg):
+            email_msg.attach('file.txt', mimetype="application/pdf")
+
     def test_dummy_backend(self):
         """
         Make sure that dummy backends returns correct number of sent messages
@@ -835,6 +853,14 @@ class MailTests(HeadersCheckMixin, SimpleTestCase):
                 with self.assertRaisesMessage(ValueError, msg):
                     sanitize_address(email_address, encoding='utf-8')
 
+    def test_email_multi_alternatives_content_mimetype_none(self):
+        email_msg = EmailMultiAlternatives()
+        msg = 'Both content and mimetype must be provided.'
+        with self.assertRaisesMessage(ValueError, msg):
+            email_msg.attach_alternative(None, 'text/html')
+        with self.assertRaisesMessage(ValueError, msg):
+            email_msg.attach_alternative('<p>content</p>', None)
+
 
 @requires_tz_support
 class MailTimeZoneTests(SimpleTestCase):