diff --git a/core/includes/theme.inc b/core/includes/theme.inc
index e8cff8b..322b882 100644
--- a/core/includes/theme.inc
+++ b/core/includes/theme.inc
@@ -727,7 +727,8 @@ function template_preprocess_links(&$variables) {
  *     to an empty string, but can be set to NULL for the attribute to be
  *     omitted. Usually, neither omission nor an empty string satisfies
  *     accessibility requirements, so it is strongly encouraged for code
- *     calling _theme('image') to pass a meaningful value for this variable.
+ *     building variables for image.html.twig templates to pass a meaningful
+ *     value for this variable.
  *     - http://www.w3.org/TR/REC-html40/struct/objects.html#h-13.8
  *     - http://www.w3.org/TR/xhtml1/dtds.html
  *     - http://dev.w3.org/html5/spec/Overview.html#alt
@@ -1721,11 +1722,12 @@ function drupal_common_theme() {
     'image' => array(
       // HTML 4 and XHTML 1.0 always require an alt attribute. The HTML 5 draft
       // allows the alt attribute to be omitted in some cases. Therefore,
-      // default the alt attribute to an empty string, but allow code calling
-      // _theme('image') to pass explicit NULL for it to be omitted. Usually,
-      // neither omission nor an empty string satisfies accessibility
-      // requirements, so it is strongly encouraged for code calling
-      // _theme('image') to pass a meaningful value for the alt variable.
+      // default the alt attribute to an empty string, but allow code providing
+      // variables to image.html.twig templates to pass explicit NULL for it to
+      // be omitted. Usually, neither omission nor an empty string satisfies
+      // accessibility requirements, so it is strongly encouraged for code
+      // building variables for image.html.twig templates to pass a meaningful
+      // value for the alt variable.
       // - http://www.w3.org/TR/REC-html40/struct/objects.html#h-13.8
       // - http://www.w3.org/TR/xhtml1/dtds.html
       // - http://dev.w3.org/html5/spec/Overview.html#alt
diff --git a/core/lib/Drupal/Core/Render/theme.api.php b/core/lib/Drupal/Core/Render/theme.api.php
index aff8ab5..471c055 100644
--- a/core/lib/Drupal/Core/Render/theme.api.php
+++ b/core/lib/Drupal/Core/Render/theme.api.php
@@ -37,16 +37,16 @@
  * http://twig.sensiolabs.org/doc/templates.html
  *
  * @section sec_theme_hooks Theme Hooks
- * The theme system is invoked in drupal_render() by calling the internal
- * _theme() function, which operates on the concept of "theme hooks". Theme
- * hooks define how a particular type of data should be rendered. They are
- * registered by modules by implementing hook_theme(), which specifies the name
- * of the hook, the input "variables" used to provide data and options, and
- * other information. Modules implementing hook_theme() also need to provide a
- * default implementation for each of their theme hooks, normally in a Twig
- * file, and they may also provide preprocessing functions. For example, the
- * core Search module defines a theme hook for a search result item in
- * search_theme():
+ * The theme system is invoked in \Drupal\Core\Render\Renderer::doRender() by
+ * calling the \Drupal\Core\Theme\ThemeManagerInterface::render() function,
+ * which operates on the concept of "theme hooks". Theme hooks define how a
+ * particular type of data should be rendered. They are registered by modules by
+ * implementing hook_theme(), which specifies the name of the hook, the input
+ * "variables" used to provide data and options, and other information. Modules
+ * implementing hook_theme() also need to provide a default implementation for
+ * each of their theme hooks, normally in a Twig file, and they may also provide
+ * preprocessing functions. For example, the core Search module defines a theme
+ * hook for a search result item in search_theme():
  * @code
  * return array(
  *   'search_result' => array(
@@ -511,7 +511,8 @@ function hook_form_system_theme_settings_alter(&$form, \Drupal\Core\Form\FormSta
  * preprocess variables for a specific theme hook, whether implemented as a
  * template or function.
  *
- * For more detailed information, see _theme().
+ * For more detailed information, see
+ * @link themeable Theme system overview topic @endlink.
  *
  * @param $variables
  *   The variables array (modify in place).
@@ -559,7 +560,8 @@ function hook_preprocess(&$variables, $hook) {
  * hook. It should only be used if a module needs to override or add to the
  * theme preprocessing for a theme hook it didn't define.
  *
- * For more detailed information, see _theme().
+ * For more detailed information, see
+ * @link themeable Theme system overview topic @endlink.
  *
  * @param $variables
  *   The variables array (modify in place).
diff --git a/core/lib/Drupal/Core/Theme/Registry.php b/core/lib/Drupal/Core/Theme/Registry.php
index 0167a74..e2a89a9 100644
--- a/core/lib/Drupal/Core/Theme/Registry.php
+++ b/core/lib/Drupal/Core/Theme/Registry.php
@@ -47,12 +47,12 @@ class Registry implements DestructableInterface {
    *   - name: The name of the extension the original theme hook originates
    *     from; e.g., 'node' for theme hook 'node' of Node module.
    *   - theme path: The effective \Drupal\Core\Theme\ActiveTheme::getPath()
-   *      during _theme(), available as
-   *      'directory' variable in templates. For functions, it should point to
-   *      the respective theme.For templates, it should point to the directory
-   *      that contains the template.
+   *      during \Drupal\Core\Theme\ThemeManagerInterface::render(), available
+   *      as 'directory' variable in templates. For functions, it should point
+   *      to the respective theme. For templates, it should point to the
+   *      directory that contains the template.
    *   - includes: (optional) An array of include files to load when the theme
-   *     hook is executed by _theme().
+   *     hook is executed by \Drupal\Core\Theme\ThemeManagerInterface::render().
    *   - file: (optional) A filename to add to 'includes', either prefixed with
    *     the value of 'path', or the path of the extension implementing
    *     hook_theme().
@@ -389,7 +389,8 @@ protected function build() {
    *     in hook_theme(). If there is more than one implementation and
    *     'render element' is not specified in a later one, then the previous
    *     definition is kept.
-   *   - 'preprocess functions': See _theme() for detailed documentation.
+   *   - See the @link themeable Theme system overview topic @endlink for
+   *     detailed documentation.
    * @param string $name
    *   The name of the module, theme engine, base theme engine, theme or base
    *   theme implementing hook_theme().
@@ -530,7 +531,8 @@ protected function processExtension(array &$cache, $name, $type, $theme, $path)
           }
           foreach ($prefixes as $prefix) {
             // Only use non-hook-specific variable preprocessors for theming
-            // hooks implemented as templates. See _theme().
+            // hooks implemented as templates. See the @defgroup themeable
+            // topic.
             if (isset($info['template']) && function_exists($prefix . '_preprocess')) {
               $info['preprocess functions'][] = $prefix . '_preprocess';
             }
@@ -566,7 +568,7 @@ protected function processExtension(array &$cache, $name, $type, $theme, $path)
             $cache[$hook]['preprocess functions'] = array();
           }
           // Only use non-hook-specific variable preprocessors for theme hooks
-          // implemented as templates. See _theme().
+          // implemented as templates. See the @defgroup themeable topic.
           if (isset($info['template']) && function_exists($name . '_preprocess')) {
             $cache[$hook]['preprocess functions'][] = $name . '_preprocess';
           }
diff --git a/core/lib/Drupal/Core/Theme/ThemeManager.php b/core/lib/Drupal/Core/Theme/ThemeManager.php
index 7e0e0b4..d4c6a2c 100644
--- a/core/lib/Drupal/Core/Theme/ThemeManager.php
+++ b/core/lib/Drupal/Core/Theme/ThemeManager.php
@@ -138,11 +138,11 @@ public function render($hook, array $variables) {
 
     $active_theme = $this->getActiveTheme();
 
-    // If called before all modules are loaded, we do not necessarily have a full
-    // theme registry to work with, and therefore cannot process the theme
+    // If called before all modules are loaded, we do not necessarily have a
+    // full theme registry to work with, and therefore cannot process the theme
     // request properly. See also \Drupal\Core\Theme\Registry::get().
     if (!$this->moduleHandler->isLoaded() && !defined('MAINTENANCE_MODE')) {
-      throw new \Exception(t('_theme() may not be called until all modules are loaded.'));
+      throw new \Exception('The theme implementations may not be rendered until all modules are loaded.');
     }
 
     $theme_registry = $this->themeRegistry->getRuntime();
@@ -180,9 +180,10 @@ public function render($hook, array $variables) {
           \Drupal::logger('theme')->warning('Theme hook %hook not found.', array('%hook' => $hook));
         }
         // There is no theme implementation for the hook passed. Return FALSE so
-        // the function calling _theme() can differentiate between a hook that
-        // exists and renders an empty string and a hook that is not
-        // implemented.
+        // the function calling
+        // \Drupal\Core\Theme\ThemeManagerInterface::render() can differentiate
+        // between a hook that exists and renders an empty string, and a hook
+        // that is not implemented.
         return FALSE;
       }
     }
@@ -233,8 +234,8 @@ public function render($hook, array $variables) {
 
     // Invoke hook_theme_suggestions_HOOK().
     $suggestions = $this->moduleHandler->invokeAll('theme_suggestions_' . $base_theme_hook, array($variables));
-    // If _theme() was invoked with a direct theme suggestion like
-    // '#theme' => 'node__article', add it to the suggestions array before
+    // If the theme implementation was invoked with a direct theme suggestion
+    // like '#theme' => 'node__article', add it to the suggestions array before
     // invoking suggestion alter hooks.
     if (isset($info['base hook'])) {
       $suggestions[] = $hook;
@@ -250,10 +251,10 @@ public function render($hook, array $variables) {
     $this->alter($hooks, $suggestions, $variables, $base_theme_hook);
 
     // Check if each suggestion exists in the theme registry, and if so,
-    // use it instead of the hook that _theme() was called with. For example, a
-    // function may call _theme('node', ...), but a module can add
-    // 'node__article' as a suggestion via hook_theme_suggestions_HOOK_alter(),
-    // enabling a theme to have an alternate template file for article nodes.
+    // use it instead of the base hook. For example, a function may use
+    // '#theme' => 'node', but a module can add 'node__article' as a suggestion
+    // via hook_theme_suggestions_HOOK_alter(), enabling a theme to have
+    // an alternate template file for article nodes.
     foreach (array_reverse($suggestions) as $suggestion) {
       if ($theme_registry->has($suggestion)) {
         $info = $theme_registry->get($suggestion);
diff --git a/core/lib/Drupal/Core/Utility/ThemeRegistry.php b/core/lib/Drupal/Core/Utility/ThemeRegistry.php
index c5e6055..1a3336e 100644
--- a/core/lib/Drupal/Core/Utility/ThemeRegistry.php
+++ b/core/lib/Drupal/Core/Utility/ThemeRegistry.php
@@ -24,15 +24,6 @@
 class ThemeRegistry extends CacheCollector implements DestructableInterface {
 
   /**
-   * Whether the partial registry can be persisted to the cache.
-   *
-   * This is only allowed if all modules and the request method is GET. _theme()
-   * should be very rarely called on POST requests and this avoids polluting
-   * the runtime cache.
-   */
-  protected $persistable;
-
-  /**
    * The complete theme registry array.
    */
   protected $completeRegistry;
diff --git a/core/modules/image/image.module b/core/modules/image/image.module
index 2c222f8..97b3dd2 100644
--- a/core/modules/image/image.module
+++ b/core/modules/image/image.module
@@ -96,11 +96,11 @@ function image_theme() {
     'image_style' => array(
       // HTML 4 and XHTML 1.0 always require an alt attribute. The HTML 5 draft
       // allows the alt attribute to be omitted in some cases. Therefore,
-      // default the alt attribute to an empty string, but allow code calling
-      // _theme('image_style') to pass explicit NULL for it to be omitted.
+      // default the alt attribute to an empty string, but allow code using
+      // '#theme' => 'image_style' to pass explicit NULL for it to be omitted.
       // Usually, neither omission nor an empty string satisfies accessibility
-      // requirements, so it is strongly encouraged for code calling
-      // _theme('image_style') to pass a meaningful value for the alt variable.
+      // requirements, so it is strongly encouraged for code using '#theme' =>
+      // 'image_style' to pass a meaningful value for the alt variable.
       // - http://www.w3.org/TR/REC-html40/struct/objects.html#h-13.8
       // - http://www.w3.org/TR/xhtml1/dtds.html
       // - http://dev.w3.org/html5/spec/Overview.html#alt
@@ -260,8 +260,8 @@ function image_style_options($include_empty = TRUE) {
  *     attribute to be omitted in some cases. Therefore, this variable defaults
  *     to an empty string, but can be set to NULL for the attribute to be
  *     omitted. Usually, neither omission nor an empty string satisfies
- *     accessibility requirements, so it is strongly encouraged for code calling
- *     _theme('image_style') to pass a meaningful value for this variable.
+ *     accessibility requirements, so it is strongly encouraged for code using
+ *     '#theme' => 'image_style' to pass a meaningful value for this variable.
  *     - http://www.w3.org/TR/REC-html40/struct/objects.html#h-13.8
  *     - http://www.w3.org/TR/xhtml1/dtds.html
  *     - http://dev.w3.org/html5/spec/Overview.html#alt
diff --git a/core/modules/simpletest/src/KernelTestBase.php b/core/modules/simpletest/src/KernelTestBase.php
index 56c800e..6210396 100644
--- a/core/modules/simpletest/src/KernelTestBase.php
+++ b/core/modules/simpletest/src/KernelTestBase.php
@@ -518,7 +518,8 @@ protected function enableModules(array $modules) {
     $module_filenames = $module_handler->getModuleList();
     $this->kernel->updateModules($module_filenames, $module_filenames);
 
-    // Ensure isLoaded() is TRUE in order to make _theme() work.
+    // Ensure isLoaded() is TRUE in order to make
+    // \Drupal\Core\Theme\ThemeManagerInterface::render() work.
     // Note that the kernel has rebuilt the container; this $module_handler is
     // no longer the $module_handler instance from above.
     $this->container->get('module_handler')->reload();
@@ -551,7 +552,8 @@ protected function disableModules(array $modules) {
     // Update the kernel to remove their services.
     $this->kernel->updateModules($module_filenames, $module_filenames);
 
-    // Ensure isLoaded() is TRUE in order to make _theme() work.
+    // Ensure isLoaded() is TRUE in order to make
+    // \Drupal\Core\Theme\ThemeManagerInterface::render() work.
     // Note that the kernel has rebuilt the container; this $module_handler is
     // no longer the $module_handler instance from above.
     $module_handler = $this->container->get('module_handler');
diff --git a/core/modules/simpletest/src/Tests/KernelTestBaseTest.php b/core/modules/simpletest/src/Tests/KernelTestBaseTest.php
index ae3742e..2187ccc 100644
--- a/core/modules/simpletest/src/Tests/KernelTestBaseTest.php
+++ b/core/modules/simpletest/src/Tests/KernelTestBaseTest.php
@@ -290,7 +290,7 @@ function testEnableModulesFixedList() {
   }
 
   /**
-   * Tests that _theme() works right after loading a module.
+   * Tests that ThemeManager works right after loading a module.
    */
   function testEnableModulesTheme() {
     /** @var \Drupal\Core\Render\RendererInterface $renderer */
@@ -301,7 +301,8 @@ function testEnableModulesTheme() {
       '#attributes' => array(),
     );
     $this->enableModules(array('system'));
-    // _theme() throws an exception if modules are not loaded yet.
+    // \Drupal\Core\Theme\ThemeManager::render() throws an exception if modules
+    // are not loaded yet.
     $this->assertTrue($renderer->renderRoot($element));
 
     $element = $original_element;
diff --git a/core/modules/system/src/Tests/Theme/ThemeTest.php b/core/modules/system/src/Tests/Theme/ThemeTest.php
index 28d47386..a84ef8f 100644
--- a/core/modules/system/src/Tests/Theme/ThemeTest.php
+++ b/core/modules/system/src/Tests/Theme/ThemeTest.php
@@ -40,7 +40,7 @@ protected function setUp() {
    * Render arrays that use a render element and templates (and hence call
    * template_preprocess()) must ensure the attributes at different occasions
    * are all merged correctly:
-   *   - $variables['attributes'] as passed in to _theme()
+   *   - $variables['attributes'] as passed in to the theme hook implementation.
    *   - the render element's #attributes
    *   - any attributes set in the template's preprocessing function
    */
@@ -57,7 +57,7 @@ function testAttributeMerging() {
   }
 
   /**
-   * Test that _theme() returns expected data types.
+   * Test that ThemeManager renders the expected data types.
    */
   function testThemeDataTypes() {
     // theme_test_false is an implemented theme hook so \Drupal::theme() service
diff --git a/core/modules/system/tests/modules/theme_test/theme_test.module b/core/modules/system/tests/modules/theme_test/theme_test.module
index 8a8841e..f64da1e 100644
--- a/core/modules/system/tests/modules/theme_test/theme_test.module
+++ b/core/modules/system/tests/modules/theme_test/theme_test.module
@@ -88,14 +88,14 @@ function template_preprocess_theme_test_function_suggestions(&$variables) {
 }
 
 /**
- * Theme function for testing _theme('theme_test_foo').
+ * Theme function for hook theme_test_foo.
  */
 function theme_theme_test_foo($variables) {
   return $variables['foo'];
 }
 
 /**
- * Theme function for testing _theme('theme_test_function_template_override').
+ * Theme function for hook theme_test_function_template_override.
  */
 function theme_theme_test_function_template_override($variables) {
   return 'theme_test_function_template_override test failed.';
@@ -140,7 +140,8 @@ function template_preprocess_theme_test_render_element(&$variables) {
  *
  * Theme hooks defining a 'render element' add an internal '#render_children'
  * property. When this property is found, drupal_render() avoids calling
- * _theme() on the top-level element to prevent infinite recursion.
+ * the 'theme.manager' service 'render' method on the top-level element to
+ * prevent infinite recursion.
  *
  * @param array $variables
  *   An associative array containing:
diff --git a/core/modules/update/src/Form/UpdateManagerUpdate.php b/core/modules/update/src/Form/UpdateManagerUpdate.php
index cafa4d1..80cc830 100644
--- a/core/modules/update/src/Form/UpdateManagerUpdate.php
+++ b/core/modules/update/src/Form/UpdateManagerUpdate.php
@@ -197,9 +197,9 @@ public function buildForm(array $form, FormStateInterface $form_state) {
 
       if ($needs_manual) {
         // There are no checkboxes in the 'Manual updates' table so it will be
-        // rendered by _theme('table'), not _theme('tableselect'). Since the data
-        // formats are incompatible, we convert now to the format expected by
-        // _theme('table').
+        // rendered by '#theme' => 'table', not '#theme' => 'tableselect'. Since
+        // the data formats are incompatible, we convert now to the format
+        // expected by '#theme' => 'table'.
         unset($entry['#weight']);
         $attributes = $entry['#attributes'];
         unset($entry['#attributes']);
diff --git a/core/tests/Drupal/KernelTests/KernelTestBase.php b/core/tests/Drupal/KernelTests/KernelTestBase.php
index fd7b864..c2d8a56 100644
--- a/core/tests/Drupal/KernelTests/KernelTestBase.php
+++ b/core/tests/Drupal/KernelTests/KernelTestBase.php
@@ -882,7 +882,8 @@ protected function disableModules(array $modules) {
     // Update the kernel to remove their services.
     $this->container->get('kernel')->updateModules($module_filenames, $module_filenames);
 
-    // Ensure isLoaded() is TRUE in order to make _theme() work.
+    // Ensure isLoaded() is TRUE in order to make
+    // \Drupal\Core\Theme\ThemeManagerInterface::render() work.
     // Note that the kernel has rebuilt the container; this $module_handler is
     // no longer the $module_handler instance from above.
     $module_handler = $this->container->get('module_handler');
diff --git a/core/themes/engines/twig/twig.engine b/core/themes/engines/twig/twig.engine
index 30ec511..b66fe58 100644
--- a/core/themes/engines/twig/twig.engine
+++ b/core/themes/engines/twig/twig.engine
@@ -37,7 +37,7 @@ function twig_init(Extension $theme) {
  *
  * Renders a Twig template.
  *
- * If the Twig debug setting is enabled, HTML comments including _theme() call
+ * If the Twig debug setting is enabled, HTML comments including the theme hook
  * and template file name suggestions will surround the template markup.
  *
  * @param string $template_file