diff -u b/core/lib/Drupal/Core/Asset/LibraryDiscoveryCollector.php b/core/lib/Drupal/Core/Asset/LibraryDiscoveryCollector.php
--- b/core/lib/Drupal/Core/Asset/LibraryDiscoveryCollector.php
+++ b/core/lib/Drupal/Core/Asset/LibraryDiscoveryCollector.php
@@ -137,7 +137,9 @@
     if (!empty($libraries_extend["$extension/$library_name"])) {
       foreach ($libraries_extend["$extension/$library_name"] as $library_extend_name) {
         if (isset($library_definition['deprecated'])) {
-          @trigger_error(sprintf('Deprecated library extend %s detected in %s.', "$extension/$library_name", $this->themeManager->getActiveTheme()->getName()), E_USER_DEPRECATED);
+          $extend_message = sprintf('Theme "%s" is extending a deprecated library.', $extension);
+          $library_deprecation = str_replace('%library_id%', "$extension/$library_name", $library_definition['deprecated']);
+          @trigger_error(sprintf('%s %s', $extend_message, $library_deprecation), E_USER_DEPRECATED);
         }
         if (!is_string($library_extend_name)) {
           // Only string library names are allowed.
diff -u b/core/lib/Drupal/Core/Asset/LibraryDiscoveryParser.php b/core/lib/Drupal/Core/Asset/LibraryDiscoveryParser.php
--- b/core/lib/Drupal/Core/Asset/LibraryDiscoveryParser.php
+++ b/core/lib/Drupal/Core/Asset/LibraryDiscoveryParser.php
@@ -383,7 +383,9 @@
         // Process libraries overrides.
         if (isset($libraries_overrides["$extension/$library_name"])) {
           if (isset($library['deprecated'])) {
-            @trigger_error(sprintf('Deprecated library override %s detected in %s.', "$extension/$library_name", $active_theme->getName()), E_USER_DEPRECATED);
+            $override_message = sprintf('Theme "%s" is overriding a deprecated library.', $extension);
+            $library_deprecation = str_replace('%library_id%', "$extension/$library_name", $library['deprecated']);
+            @trigger_error(sprintf('%s %s', $override_message, $library_deprecation), E_USER_DEPRECATED);
           }
           // Active theme defines an override for this library.
           $override_definition = $libraries_overrides["$extension/$library_name"];
only in patch2:
unchanged:
--- a/core/modules/system/tests/modules/theme_test/theme_test.libraries.yml
+++ b/core/modules/system/tests/modules/theme_test/theme_test.libraries.yml
@@ -5,3 +5,17 @@ theme_stylesheets_override_and_remove_test:
       css/base-remove.css: {}
       css/sub-override.css: {}
       css/sub-remove.css: {}
+
+deprecated_library:
+  version: VERSION
+  css:
+    base:
+      css/foo.css: {}
+  deprecated: 'The "%library_id%" asset library is deprecated in drupal:9.1.0 and is removed from drupal:9.0.0. Use another library instead. See https://www.example.com'
+
+another_deprecated_library:
+  version: VERSION
+  css:
+    base:
+      css/bar.css: {}
+  deprecated: 'The "%library_id%" asset library is deprecated in drupal:9.1.0 and is removed from drupal:9.0.0. Use another library instead. See https://www.example.com'
only in patch2:
unchanged:
--- a/core/modules/system/tests/themes/test_legacy_theme/test_legacy_theme.info.yml
+++ b/core/modules/system/tests/themes/test_legacy_theme/test_legacy_theme.info.yml
@@ -4,3 +4,13 @@ description: 'Test theme to test deprecated functionality.'
 version: VERSION
 package: Testing
 base theme: test_theme
+
+libraries-override:
+  theme_test/deprecated_library:
+    css:
+      base:
+        css/foo.css: css/bar.css
+
+libraries-extend:
+  theme_test/another_deprecated_library:
+    - test_legacy_theme/library
only in patch2:
unchanged:
--- /dev/null
+++ b/core/modules/system/tests/themes/test_legacy_theme/test_legacy_theme.libraries.yml
@@ -0,0 +1,4 @@
+library:
+  css:
+    base:
+      css/baz.css: {}
only in patch2:
unchanged:
--- a/core/tests/Drupal/KernelTests/Core/Asset/LibraryDiscoveryIntegrationTest.php
+++ b/core/tests/Drupal/KernelTests/Core/Asset/LibraryDiscoveryIntegrationTest.php
@@ -20,6 +20,11 @@ class LibraryDiscoveryIntegrationTest extends KernelTestBase {
    */
   protected $libraryDiscovery;
 
+  /**
+   * {@inheritdoc}
+   */
+ protected static $modules = ['theme_test'];
+
   /**
    * {@inheritdoc}
    */
@@ -208,6 +213,33 @@ public function testLibrariesExtend() {
     }
   }
 
+  /**
+   * Test deprecated libraries.
+   */
+  public function testDeprecatedLibrary() {
+    $deprecations = [];
+    set_error_handler(function ($severity, $message) use (&$deprecations) {
+      // Convert deprecation error into a catchable exception.
+      if ($severity === E_USER_DEPRECATED) {
+        $deprecations[] = $message;
+        return function() { return true; };
+      }
+    });
+
+    $this->activateTheme('test_legacy_theme');
+    $this->libraryDiscovery->getLibraryByName('theme_test', 'deprecated_library');
+    $this->libraryDiscovery->getLibraryByName('theme_test', 'another_deprecated_library');
+    $expected_derecations = [
+      'Theme "theme_test" is overriding a deprecated library. The "theme_test/deprecated_library" asset library is deprecated in drupal:9.1.0 and is removed from drupal:9.0.0. Use another library instead. See https://www.example.com',
+      'Theme "theme_test" is extending a deprecated library. The "theme_test/another_deprecated_library" asset library is deprecated in drupal:9.1.0 and is removed from drupal:9.0.0. Use another library instead. See https://www.example.com',
+      'The "theme_test/deprecated_library" asset library is deprecated in drupal:9.1.0 and is removed from drupal:9.0.0. Use another library instead. See https://www.example.com',
+      'The "theme_test/another_deprecated_library" asset library is deprecated in drupal:9.1.0 and is removed from drupal:9.0.0. Use another library instead. See https://www.example.com',
+    ];
+    $this->assertSame($expected_derecations, $deprecations);
+
+    restore_error_handler();
+  }
+
   /**
    * Activates a specified theme.
    *
only in patch2:
unchanged:
--- a/core/tests/Drupal/Tests/Core/Asset/LibraryDiscoveryCollectorTest.php
+++ b/core/tests/Drupal/Tests/Core/Asset/LibraryDiscoveryCollectorTest.php
@@ -61,6 +61,23 @@ class LibraryDiscoveryCollectorTest extends UnitTestCase {
       'js' => [],
       'css' => [],
     ],
+    'test_3' => [
+      'js' => [],
+      'css' => [
+        'theme' => [
+          'foo.css' => [],
+        ],
+      ],
+    ],
+    'test_4' => [
+      'js' => [],
+      'css' => [
+        'theme' => [
+          'bar.css' => [],
+        ],
+      ],
+      'deprecated' => 'The "%library_id%" asset library is deprecated in drupal:9.1.0 and is removed from drupal:9.0.0. Use the test_3 library instead. See https://www.example.com',
+    ],
   ];
 
   protected $activeTheme;
@@ -77,7 +94,6 @@ protected function setUp(): void {
     $this->libraryDiscoveryParser = $this->getMockBuilder('Drupal\Core\Asset\LibraryDiscoveryParser')
       ->disableOriginalConstructor()
       ->getMock();
-
   }
 
   /**
@@ -89,7 +105,7 @@ public function testResolveCacheMiss() {
     $this->activeTheme = $this->getMockBuilder('Drupal\Core\Theme\ActiveTheme')
       ->disableOriginalConstructor()
       ->getMock();
-    $this->themeManager->expects($this->exactly(3))
+    $this->themeManager->expects($this->exactly(5))
       ->method('getActiveTheme')
       ->willReturn($this->activeTheme);
     $this->activeTheme->expects($this->once())
@@ -115,7 +131,7 @@ public function testDestruct() {
     $this->activeTheme = $this->getMockBuilder('Drupal\Core\Theme\ActiveTheme')
       ->disableOriginalConstructor()
       ->getMock();
-    $this->themeManager->expects($this->exactly(3))
+    $this->themeManager->expects($this->exactly(5))
       ->method('getActiveTheme')
       ->willReturn($this->activeTheme);
     $this->activeTheme->expects($this->once())
@@ -150,4 +166,94 @@ public function testDestruct() {
     $this->libraryDiscoveryCollector->destruct();
   }
 
+  /**
+   * Tests library with an extend.
+   *
+   * @covers ::applyLibrariesExtend
+   */
+  public function testLibrariesExtend() {
+    $this->activeTheme = $this->getMockBuilder('Drupal\Core\Theme\ActiveTheme')
+      ->disableOriginalConstructor()
+      ->getMock();
+    $this->themeManager->expects($this->any())
+      ->method('getActiveTheme')
+      ->willReturn($this->activeTheme);
+    $this->activeTheme->expects($this->once())
+      ->method('getName')
+      ->willReturn('kitten_theme');
+    $this->activeTheme->expects($this->atLeastOnce())
+      ->method('getLibrariesExtend')
+      ->willReturn([
+        'test/test_3' => [
+          'kitten_theme/extend'
+        ],
+      ]);
+    $this->libraryDiscoveryParser->expects($this->at(0))
+      ->method('buildByExtension')
+      ->with('test')
+      ->willReturn($this->libraryData);
+    $this->libraryDiscoveryParser->expects($this->at(1))
+      ->method('buildByExtension')
+      ->with('kitten_theme')
+      ->willReturn([
+        'extend' => [
+          'css' => [
+            'theme' => [
+              'baz.css' => []
+            ],
+          ],
+        ],
+      ]);
+    $library_discovery_collector = new LibraryDiscoveryCollector($this->cache, $this->lock, $this->libraryDiscoveryParser, $this->themeManager);
+    $libraries = $library_discovery_collector->get('test');
+    $this->assertSame(['foo.css', 'baz.css'], array_keys($libraries['test_3']['css']['theme']));
+  }
+
+  /**
+   * Tests a deprecated library with an extend.
+   *
+   * @covers ::applyLibrariesExtend
+   */
+  public function testLibrariesExtendDeprecated() {
+    $previous_error_handler = set_error_handler(function ($severity, $message, $file, $line, $context) use (&$previous_error_handler) {
+      // Convert deprecation error into a catchable exception.
+      if ($severity === E_USER_DEPRECATED) {
+        throw new \ErrorException($message, 0, $severity, $file, $line);
+      }
+      if ($previous_error_handler) {
+        return $previous_error_handler($severity, $message, $file, $line, $context);
+      }
+    });
+
+    $this->activeTheme = $this->getMockBuilder('Drupal\Core\Theme\ActiveTheme')
+      ->disableOriginalConstructor()
+      ->getMock();
+    $this->themeManager->expects($this->any())
+      ->method('getActiveTheme')
+      ->willReturn($this->activeTheme);
+    $this->activeTheme->expects($this->once())
+      ->method('getName')
+      ->willReturn('kitten_theme');
+    $this->activeTheme->expects($this->atLeastOnce())
+      ->method('getLibrariesExtend')
+      ->willReturn([
+        'test/test_4' => [
+          'kitten_theme/extend'
+        ],
+      ]);
+    $this->libraryDiscoveryParser->expects($this->at(0))
+      ->method('buildByExtension')
+      ->with('test')
+      ->willReturn($this->libraryData);
+    $library_discovery_collector = new LibraryDiscoveryCollector($this->cache, $this->lock, $this->libraryDiscoveryParser, $this->themeManager);
+    try {
+      $library_discovery_collector->get('test');
+      $this->fail('No deprecation error triggered.');
+    }
+    catch (\ErrorException $e) {
+      $this->assertSame('Theme "test" is extending a deprecated library. The "test/test_4" asset library is deprecated in drupal:9.1.0 and is removed from drupal:9.0.0. Use the test_3 library instead. See https://www.example.com', $e->getMessage());
+    }
+
+    restore_error_handler();
+  }
 }
only in patch2:
unchanged:
--- a/core/tests/Drupal/Tests/Core/Asset/LibraryDiscoveryParserTest.php
+++ b/core/tests/Drupal/Tests/Core/Asset/LibraryDiscoveryParserTest.php
@@ -49,6 +49,13 @@ class LibraryDiscoveryParserTest extends UnitTestCase {
    */
   protected $themeManager;
 
+  /**
+   * The mocked active theme.
+   *
+   * @var \Drupal\Core\Theme\ActiveTheme|\PHPUnit\Framework\MockObject\MockObject
+   */
+  protected $activeTheme;
+
   /**
    * The mocked lock backend.
    *
@@ -78,15 +85,15 @@ protected function setUp(): void {
 
     $this->moduleHandler = $this->createMock('Drupal\Core\Extension\ModuleHandlerInterface');
     $this->themeManager = $this->createMock('Drupal\Core\Theme\ThemeManagerInterface');
-    $mock_active_theme = $this->getMockBuilder('Drupal\Core\Theme\ActiveTheme')
+    $this->activeTheme = $this->getMockBuilder('Drupal\Core\Theme\ActiveTheme')
       ->disableOriginalConstructor()
       ->getMock();
-    $mock_active_theme->expects($this->any())
+    $this->activeTheme->expects($this->any())
       ->method('getLibrariesOverride')
       ->willReturn([]);
     $this->themeManager->expects($this->any())
       ->method('getActiveTheme')
-      ->willReturn($mock_active_theme);
+      ->willReturn($this->activeTheme);
     $this->streamWrapperManager = $this->createMock(StreamWrapperManagerInterface::class);
     $this->librariesDirectoryFileFinder = $this->createMock(LibrariesDirectoryFileFinder::class);
     $this->libraryDiscoveryParser = new TestLibraryDiscoveryParser($this->root, $this->moduleHandler, $this->themeManager, $this->streamWrapperManager, $this->librariesDirectoryFileFinder);
@@ -111,7 +118,7 @@ public function testBuildByExtensionSimple() {
     $library = $libraries['example'];
 
     $this->assertCount(0, $library['js']);
-    $this->assertCount(1, $library['css']);
+    $this->assertCount(2, $library['css']);
     $this->assertCount(0, $library['dependencies']);
     $this->assertEquals($path . '/css/example.css', $library['css'][0]['data']);
 
@@ -544,6 +551,113 @@ public function testLibraryWithLicenses() {
     $this->assertEquals($library['license'], $expected_license);
   }
 
+  /**
+   * Tests libraries with overrides.
+   *
+   * @covers ::applyLibrariesOverride
+   */
+  public function testLibraryOverride() {
+    $mock_theme_path = 'mocked_themes/kittens';
+    $this->themeManager = $this->createMock('Drupal\Core\Theme\ThemeManagerInterface');
+    $this->activeTheme = $this->getMockBuilder('Drupal\Core\Theme\ActiveTheme')
+      ->disableOriginalConstructor()
+      ->getMock();
+    $this->activeTheme->expects($this->atLeastOnce())
+      ->method('getLibrariesOverride')
+      ->willReturn([
+        $mock_theme_path => [
+          'example_module/example' => [
+            'css' => [
+              'theme' => [
+                'css/example.css' => 'css/overridden.css',
+                'css/example2.css' => FALSE,
+              ],
+            ],
+          ],
+        ],
+      ]);
+    $this->themeManager->expects($this->any())
+      ->method('getActiveTheme')
+      ->willReturn($this->activeTheme);
+    $this->libraryDiscoveryParser = new TestLibraryDiscoveryParser($this->root, $this->moduleHandler, $this->themeManager, $this->streamWrapperManager, $this->librariesDirectoryFileFinder);
+
+    $this->moduleHandler->expects($this->atLeastOnce())
+      ->method('moduleExists')
+      ->with('example_module')
+      ->will($this->returnValue(TRUE));
+
+    $path = __DIR__ . '/library_test_files';
+    $path = substr($path, strlen($this->root) + 1);
+    $this->libraryDiscoveryParser->setPaths('module', 'example_module', $path);
+
+    $libraries = $this->libraryDiscoveryParser->buildByExtension('example_module');
+    $library = $libraries['example'];
+
+    $this->assertCount(0, $library['js']);
+    $this->assertCount(1, $library['css']);
+    $this->assertCount(0, $library['dependencies']);
+    $this->assertEquals($mock_theme_path . '/css/overridden.css', $library['css'][0]['data']);
+  }
+
+  /**
+   * Tests deprecated library with an override.
+   *
+   * @covers ::applyLibrariesOverride
+   */
+  public function testLibraryOverrideDeprecated() {
+    $previous_error_handler = set_error_handler(function ($severity, $message, $file, $line, $context) use (&$previous_error_handler) {
+      // Convert deprecation error into a catchable exception.
+      if ($severity === E_USER_DEPRECATED) {
+        throw new \ErrorException($message, 0, $severity, $file, $line);
+      }
+      if ($previous_error_handler) {
+        return $previous_error_handler($severity, $message, $file, $line, $context);
+      }
+    });
+
+    $mock_theme_path = 'mocked_themes/kittens';
+    $this->themeManager = $this->createMock('Drupal\Core\Theme\ThemeManagerInterface');
+    $this->activeTheme = $this->getMockBuilder('Drupal\Core\Theme\ActiveTheme')
+      ->disableOriginalConstructor()
+      ->getMock();
+    $this->activeTheme->expects($this->atLeastOnce())
+      ->method('getLibrariesOverride')
+      ->willReturn([
+        $mock_theme_path => [
+          'deprecated/deprecated' => [
+            'css' => [
+              'theme' => [
+                'css/example.css' => 'css/overridden.css',
+              ],
+            ],
+          ],
+        ],
+      ]);
+    $this->themeManager->expects($this->any())
+      ->method('getActiveTheme')
+      ->willReturn($this->activeTheme);
+    $this->libraryDiscoveryParser = new TestLibraryDiscoveryParser($this->root, $this->moduleHandler, $this->themeManager, $this->streamWrapperManager, $this->librariesDirectoryFileFinder);
+
+    $this->moduleHandler->expects($this->atLeastOnce())
+      ->method('moduleExists')
+      ->with('deprecated')
+      ->will($this->returnValue(TRUE));
+
+    $path = __DIR__ . '/library_test_files';
+    $path = substr($path, strlen($this->root) + 1);
+    $this->libraryDiscoveryParser->setPaths('module', 'deprecated', $path);
+
+    try {
+      $this->libraryDiscoveryParser->buildByExtension('deprecated');
+      $this->fail('No deprecation error triggered.');
+    }
+    catch (\ErrorException $e) {
+      $this->assertSame('Theme "deprecated" is overriding a deprecated library. The "deprecated/deprecated" asset library is deprecated in drupal:9.1.0 and is removed from drupal:10.0.0. Use another library instead. See https://www.example.com', $e->getMessage());
+    }
+
+    restore_error_handler();
+  }
+
   /**
    * Verifies assertions catch invalid CSS declarations.
    *
only in patch2:
unchanged:
--- /dev/null
+++ b/core/tests/Drupal/Tests/Core/Asset/library_test_files/deprecated.libraries.yml
@@ -0,0 +1,6 @@
+deprecated:
+  version: VERSION
+  css:
+    theme:
+      css/example.css: {}
+  deprecated: 'The "%library_id%" asset library is deprecated in drupal:9.1.0 and is removed from drupal:10.0.0. Use another library instead. See https://www.example.com'
only in patch2:
unchanged:
--- a/core/tests/Drupal/Tests/Core/Asset/library_test_files/example_module.libraries.yml
+++ b/core/tests/Drupal/Tests/Core/Asset/library_test_files/example_module.libraries.yml
@@ -3,3 +3,4 @@ example:
   css:
     theme:
       css/example.css: {}
+      css/example2.css: {}