diff --git a/core/includes/theme.inc b/core/includes/theme.inc
index f136ca1..f2c3ac1 100644
--- a/core/includes/theme.inc
+++ b/core/includes/theme.inc
@@ -2296,6 +2296,7 @@ function drupal_common_theme() {
     ),
     'indentation' => array(
       'variables' => array('size' => 1),
+      'function' => 'theme_indentation',
     ),
     // From theme.maintenance.inc.
     'maintenance_page' => array(
@@ -2312,9 +2313,15 @@ function drupal_common_theme() {
     ),
     'authorize_message' => array(
       'variables' => array('message' => NULL, 'success' => TRUE),
+      'function' => 'theme_authorize_message',
+      'path' => 'core/includes',
+      'file' => 'theme.maintenance.inc',
     ),
     'authorize_report' => array(
       'variables' => array('messages' => array()),
+      'function' => 'theme_authorize_report',
+      'path' => 'core/includes',
+      'file' => 'theme.maintenance.inc',
     ),
     // From pager.inc.
     'pager' => array(
diff --git a/core/lib/Drupal/Core/Theme/Registry.php b/core/lib/Drupal/Core/Theme/Registry.php
index da3122c..8c9efb3 100644
--- a/core/lib/Drupal/Core/Theme/Registry.php
+++ b/core/lib/Drupal/Core/Theme/Registry.php
@@ -401,6 +401,9 @@ protected function build() {
    * @see _theme()
    * @see hook_theme()
    * @see list_themes()
+   * @see twig_render_template()
+   *
+   * @throws \BadFunctionCallException
    */
   protected function processExtension(&$cache, $name, $type, $theme, $path) {
     $result = array();
@@ -430,12 +433,6 @@ protected function processExtension(&$cache, $name, $type, $theme, $path) {
         $result[$hook]['type'] = $type;
         $result[$hook]['theme path'] = $path;
 
-        // If function and file are omitted, default to standard naming
-        // conventions.
-        if (!isset($info['template']) && !isset($info['function'])) {
-          $result[$hook]['function'] = ($type == 'module' ? 'theme_' : $name . '_') . $hook;
-        }
-
         if (isset($cache[$hook]['includes'])) {
           $result[$hook]['includes'] = $cache[$hook]['includes'];
         }
@@ -451,20 +448,37 @@ protected function processExtension(&$cache, $name, $type, $theme, $path) {
           $result[$hook]['includes'][] = $include_file;
         }
 
+        // A template file is the default implementation for a theme hook, but
+        // if the theme hook specifies a function callback instead, check to
+        // ensure the function actually exists.
+        if (isset($info['function']) && !function_exists($info['function'])) {
+          throw new \BadFunctionCallException(sprintf(
+            'Theme hook "%s" refers to a theme function callback that does not exist: "%s"',
+            $hook,
+            $info['function']
+          ));
+        }
+        // Provide a default naming convention for 'template' based on the
+        // hook used. If the template does not exist, the theme engine used
+        // should throw an exception at runtime when attempting to include
+        // the template file.
+        elseif (!isset($info['template'])) {
+          $info['template'] = strtr($hook, '_', '-');
+          $result[$hook]['template'] = $info['template'];
+        }
+
+        // Prepend the current theming path when none is set. This is required
+        // for the default theme engine to know where the template lives.
+        if (isset($result[$hook]['template']) && !isset($info['path'])) {
+          $result[$hook]['path'] = $path . '/templates';
+        }
+
         // If the default keys are not set, use the default values registered
         // by the module.
         if (isset($cache[$hook])) {
           $result[$hook] += array_intersect_key($cache[$hook], $hook_defaults);
         }
 
-        // The following apply only to theming hooks implemented as templates.
-        if (isset($info['template'])) {
-          // Prepend the current theming path when none is set.
-          if (!isset($info['path'])) {
-            $result[$hook]['template'] = $path . '/templates/' . $info['template'];
-          }
-        }
-
         // Preprocess variables for all theming hooks, whether the hook is
         // implemented as a template or as a function. Ensure they are arrays.
         if (!isset($info['preprocess functions']) || !is_array($info['preprocess functions'])) {
diff --git a/core/modules/book/book.module b/core/modules/book/book.module
index 5fd5d21..6769c3a 100644
--- a/core/modules/book/book.module
+++ b/core/modules/book/book.module
@@ -62,6 +62,7 @@ function book_theme() {
     ),
     'book_link' => array(
       'render element' => 'element',
+      'function' => 'theme_book_link',
     ),
     'book_export_html' => array(
       'variables' => array('title' => NULL, 'contents' => NULL, 'depth' => NULL),
@@ -70,6 +71,7 @@ function book_theme() {
     'book_admin_table' => array(
       'render element' => 'form',
       'file' => 'book.admin.inc',
+      'function' => 'theme_book_admin_table',
     ),
     'book_all_books_block' => array(
       'render element' => 'book_menus',
diff --git a/core/modules/field_ui/field_ui.module b/core/modules/field_ui/field_ui.module
index 5bce9dd..5721172 100644
--- a/core/modules/field_ui/field_ui.module
+++ b/core/modules/field_ui/field_ui.module
@@ -66,6 +66,7 @@ function field_ui_theme() {
   return array(
     'field_ui_table' => array(
       'render element' => 'elements',
+      'function' => 'theme_field_ui_table',
     ),
   );
 }
diff --git a/core/modules/language/language.module b/core/modules/language/language.module
index 40b9bfa..7fa87b7 100644
--- a/core/modules/language/language.module
+++ b/core/modules/language/language.module
@@ -100,10 +100,12 @@ function language_theme() {
     'language_negotiation_configure_browser_form_table' => array(
       'render element' => 'form',
       'file' => 'language.admin.inc',
+      'function' => 'theme_language_negotiation_configure_browser_form_table',
     ),
     'language_content_settings_table' => array(
       'render element' => 'element',
       'file' => 'language.admin.inc',
+      'function' => 'theme_language_content_settings_table',
     ),
   );
 }
diff --git a/core/modules/locale/locale.module b/core/modules/locale/locale.module
index a6b785e..54d5477 100644
--- a/core/modules/locale/locale.module
+++ b/core/modules/locale/locale.module
@@ -181,6 +181,7 @@ function locale_theme() {
     'locale_translate_edit_form_strings' => array(
       'render element' => 'form',
       'file' => 'locale.pages.inc',
+      'function' => 'theme_locale_translate_edit_form_strings',
     ),
     'locale_translation_last_check' => array(
       'variables' => array('last' => NULL),
diff --git a/core/modules/menu_ui/menu_ui.module b/core/modules/menu_ui/menu_ui.module
index 148203a..cc9eb79 100644
--- a/core/modules/menu_ui/menu_ui.module
+++ b/core/modules/menu_ui/menu_ui.module
@@ -78,6 +78,7 @@ function menu_ui_theme() {
     'menu_overview_form' => array(
       'file' => 'menu_ui.admin.inc',
       'render element' => 'form',
+      'function' => 'theme_menu_overview_form',
     ),
   );
 }
diff --git a/core/modules/node/node.module b/core/modules/node/node.module
index c51640c..3d7a521 100644
--- a/core/modules/node/node.module
+++ b/core/modules/node/node.module
@@ -141,6 +141,7 @@ function node_theme() {
     ),
     'node_search_admin' => array(
       'render element' => 'form',
+      'function' => 'theme_node_search_admin',
     ),
     'node_add_list' => array(
       'variables' => array('content' => NULL),
diff --git a/core/modules/responsive_image/responsive_image.module b/core/modules/responsive_image/responsive_image.module
index 63c732a..13f3b45 100644
--- a/core/modules/responsive_image/responsive_image.module
+++ b/core/modules/responsive_image/responsive_image.module
@@ -80,6 +80,7 @@ function responsive_image_theme() {
         'attributes' => array(),
         'mapping_id' => array(),
       ),
+      'function' => 'theme_responsive_image',
     ),
     'responsive_image_formatter' => array(
       'variables' => array(
@@ -88,6 +89,7 @@ function responsive_image_theme() {
         'image_style' => NULL,
         'mapping_id' => array(),
       ),
+      'function' => 'theme_responsive_image_formatter',
     ),
     'responsive_image_source' => array(
       'variables' => array(
@@ -96,6 +98,7 @@ function responsive_image_theme() {
         'dimensions' => NULL,
         'media' => NULL,
       ),
+      'function' => 'theme_responsive_image_source',
     ),
   );
 }
diff --git a/core/modules/system/system.api.php b/core/modules/system/system.api.php
index ebe1b15..c6a2281 100644
--- a/core/modules/system/system.api.php
+++ b/core/modules/system/system.api.php
@@ -980,17 +980,20 @@ function hook_help($route_name, \Drupal\Core\Routing\RouteMatchInterface $route_
  *     theme path will be used, but if the file will not be in the default
  *     path, include it here. This path should be relative to the Drupal root
  *     directory.
- *   - template: If specified, this theme implementation is a template, and
- *     this is the template file without an extension. Do not put .html.twig on
- *     this file; that extension will be added automatically by the default
- *     rendering engine (which is Twig). If 'path' above is specified, the
- *     template should also be in this path.
+ *   - template: If specified, the theme implementation is a template file, and
+ *     this is the template name. Do not add 'html.twig' on the end of the
+ *     template name. The extension will be added automatically by the default
+ *     rendering engine (which is Twig.) If 'path' is specified, 'template'
+ *     should also be specified. If neither 'template' nor 'function' are
+ *     specified, a default template name will be assumed. For example, if a
+ *     module registers the 'search_result' theme hook, 'search-result' will be
+ *     assigned as its template name.
  *   - function: If specified, this will be the function name to invoke for
  *     this implementation. If neither 'template' nor 'function' is specified,
- *     a default function name will be assumed. For example, if a module
- *     registers the 'node' theme hook, 'theme_node' will be assigned to its
- *     function. If the chameleon theme registers the node hook, it will be
- *     assigned 'chameleon_node' as its function.
+ *     a default template name will be assumed. If neither 'template' nor
+ *     'function' are specified, a default template name will be assumed. For
+ *     example, if a module registers the 'search_result' theme hook,
+ *     'search-result' will be assigned as its template name.
  *   - base hook: Used for _theme() suggestions only: the base theme hook name.
  *     Instead of this suggestion's implementation being used directly, the base
  *     hook will be invoked with this implementation as its first suggestion.
diff --git a/core/modules/system/system.module b/core/modules/system/system.module
index b478fb4..b4a2737 100644
--- a/core/modules/system/system.module
+++ b/core/modules/system/system.module
@@ -187,10 +187,12 @@ function system_theme() {
     'system_modules_details' => array(
       'render element' => 'form',
       'file' => 'system.admin.inc',
+      'function' => 'theme_system_modules_details',
     ),
     'system_modules_uninstall' => array(
       'render element' => 'form',
       'file' => 'system.admin.inc',
+      'function' => 'theme_system_modules_uninstall',
     ),
     'status_report' => array(
       'variables' => array('requirements' => NULL),
@@ -219,6 +221,7 @@ function system_theme() {
     ),
     'system_compact_link' => array(
       'variables' => array(),
+      'function' => 'theme_system_compact_link',
     ),
   ));
 }
diff --git a/core/modules/system/tests/modules/common_test/common_test.module b/core/modules/system/tests/modules/common_test/common_test.module
index bd17563..e23a842 100644
--- a/core/modules/system/tests/modules/common_test/common_test.module
+++ b/core/modules/system/tests/modules/common_test/common_test.module
@@ -123,6 +123,7 @@ function common_test_theme() {
     ),
     'common_test_empty' => array(
       'variables' => array('foo' => 'foo'),
+      'function' => 'theme_common_test_empty',
     ),
   );
 }
diff --git a/core/modules/system/tests/modules/theme_suggestions_test/theme_suggestions_test.module b/core/modules/system/tests/modules/theme_suggestions_test/theme_suggestions_test.module
index e963c2f..974856a 100644
--- a/core/modules/system/tests/modules/theme_suggestions_test/theme_suggestions_test.module
+++ b/core/modules/system/tests/modules/theme_suggestions_test/theme_suggestions_test.module
@@ -12,6 +12,7 @@ function theme_suggestions_test_theme() {
   $items['theme_suggestions_test_include'] = array(
     'file' => 'theme_suggestions_test.inc',
     'variables' => array(),
+    'function' => 'theme_theme_suggestions_test_include',
   );
   return $items;
 }
diff --git a/core/modules/system/tests/modules/theme_test/theme_test.module b/core/modules/system/tests/modules/theme_test/theme_test.module
index dd71fb7..8616f02 100644
--- a/core/modules/system/tests/modules/theme_test/theme_test.module
+++ b/core/modules/system/tests/modules/theme_test/theme_test.module
@@ -9,6 +9,7 @@ function theme_test_theme($existing, $type, $theme, $path) {
   $items['theme_test'] = array(
     'file' => 'theme_test.inc',
     'variables' => array('foo' => ''),
+    'function' => 'theme_theme_test',
   );
   $items['theme_test_template_test'] = array(
     'template' => 'theme_test.template_test',
@@ -34,12 +35,15 @@ function theme_test_theme($existing, $type, $theme, $path) {
   );
   $items['theme_test_function_suggestions'] = array(
     'variables' => array(),
+    'function' => 'theme_theme_test_function_suggestions',
   );
   $items['theme_test_suggestions_include'] = array(
     'variables' => array(),
+    'function' => 'theme_theme_test_suggestions_include',
   );
   $items['theme_test_foo'] = array(
     'variables' => array('foo' => NULL),
+    'function' => 'theme_theme_test_foo',
   );
   $items['theme_test_render_element'] = array(
     'render element' => 'elements',
@@ -47,9 +51,11 @@ function theme_test_theme($existing, $type, $theme, $path) {
   );
   $items['theme_test_render_element_children'] = array(
     'render element' => 'element',
+    'function' => 'theme_theme_test_render_element_children',
   );
   $items['theme_test_function_template_override'] = array(
     'variables' => array(),
+    'function' => 'theme_theme_test_function_template_override',
   );
   $info['test_theme_not_existing_function'] = array(
     'function' => 'test_theme_not_existing_function',
diff --git a/core/modules/toolbar/toolbar.module b/core/modules/toolbar/toolbar.module
index b9174bc..ff81d67 100644
--- a/core/modules/toolbar/toolbar.module
+++ b/core/modules/toolbar/toolbar.module
@@ -41,9 +41,6 @@ function toolbar_theme($existing, $type, $theme, $path) {
     'render element' => 'element',
     'template' => 'toolbar',
   );
-  $items['toolbar_item'] = array(
-    'render element' => 'element',
-  );
 
   return $items;
 }
diff --git a/core/modules/update/update.module b/core/modules/update/update.module
index 64a4255..1da3425 100644
--- a/core/modules/update/update.module
+++ b/core/modules/update/update.module
@@ -204,11 +204,11 @@ function update_theme() {
       'file' => 'update.report.inc',
       'template' => 'update-project-status',
     ),
+    // We are using template instead of '#type' => 'table' here to keep markup
+    // out of preprocess and allow for easier changes to markup.
     'update_version' => array(
       'variables' => array('version' => NULL, 'title' => NULL, 'attributes' => array()),
       'file' => 'update.report.inc',
-      // We are using template instead of '#type' => 'table' here to keep markup
-      // out of preprocess and allow for easier changes to markup.
       'template' => 'update-version',
     ),
   );
diff --git a/core/modules/views/views.module b/core/modules/views/views.module
index 84b324f..dda2b55 100644
--- a/core/modules/views/views.module
+++ b/core/modules/views/views.module
@@ -145,6 +145,7 @@ function views_theme($existing, $type, $theme, $path) {
   // Default view themes
   $hooks['views_view_field'] = $base + array(
     'variables' => array('view' => NULL, 'field' => NULL, 'row' => NULL),
+    'function' => 'theme_views_view_field',
   );
   $hooks['views_view_grouping'] = $base + array(
     'variables' => array('view' => NULL, 'grouping' => NULL, 'grouping_level' => NULL, 'rows' => NULL, 'title' => NULL),
@@ -165,9 +166,9 @@ function views_theme($existing, $type, $theme, $path) {
       if (!isset($def['theme']) || empty($def['register_theme'])) {
         continue;
       }
-      // For each theme registration we a base directory to look for the
-      // templates folder. This will be in any case the root of the given module
-      // so we always need a module definition.
+      // For each theme registration, we have a base directory to check for the
+      // templates folder. This will be relative to the root of the given module
+      // folder, so we always need a module definition.
       // @todo: watchdog or exception?
       if (!isset($def['provider']) || !$module_handler->moduleExists($def['provider'])) {
         continue;
@@ -177,35 +178,44 @@ function views_theme($existing, $type, $theme, $path) {
         'variables' => $variables[$type],
       );
 
-      // For the views module we ensure views.theme.inc is included.
-      if ($def['provider'] == 'views') {
-        $def['theme_file'] = 'views.theme.inc';
-      }
       // We always use the module directory as base dir.
       $module_dir = drupal_get_path('module', $def['provider']);
+      $hooks[$def['theme']]['path'] = $module_dir;
 
+      // For the views module we ensure views.theme.inc is included.
+      if ($def['provider'] == 'views') {
+        if (!isset($hooks[$def['theme']]['includes'])) {
+          $hooks[$def['theme']]['includes'] = array();
+        }
+        if (!in_array('views.theme.inc', $hooks[$def['theme']]['includes'])) {
+          $hooks[$def['theme']]['includes'][] = $module_dir . '/views.theme.inc';
+        }
+      }
       // The theme_file definition is always relative to the modules directory.
-      if (isset($def['theme_file'])) {
-        $hooks[$def['theme']]['path'] = $module_dir;
+      elseif (!empty($def['theme_file'])) {
         $hooks[$def['theme']]['file'] = $def['theme_file'];
       }
-      // Whenever we got a theme file, we include it directly so we can
+
+      // Whenever we have a theme file, we include it directly so we can
       // auto-detect the theme function.
       if (isset($def['theme_file'])) {
-        $include = DRUPAL_ROOT . '/' . $module_dir. '/' . $def['theme_file'];
+        $include = DRUPAL_ROOT . '/' . $module_dir . '/' . $def['theme_file'];
         if (is_file($include)) {
           require_once $include;
         }
       }
-     // If there is no theme function for the given theme definition, we assume
-     // a template file shall be used. By default this file is located in the
-     // /templates directory of the module's folder.
-     // If a module wants to define its own location it has to set
-     // register_theme of the plugin to FALSE and implement hook_theme() by
-     // itself.
+
+      // If there is no theme function for the given theme definition, it must
+      // be a template file. By default this file is located in the /templates
+      // directory of the module's folder. If a module wants to define its own
+      // location it has to set register_theme of the plugin to FALSE and
+      // implement hook_theme() by itself.
       if (!function_exists('theme_' . $def['theme'])) {
-        $hooks[$def['theme']]['path'] = $module_dir;
-        $hooks[$def['theme']]['template'] = 'templates/' . drupal_clean_css_identifier($def['theme']);
+        $hooks[$def['theme']]['path'] .= '/templates';
+        $hooks[$def['theme']]['template'] = drupal_clean_css_identifier($def['theme']);
+      }
+      else {
+        $hooks[$def['theme']]['function'] = 'theme_' . $def['theme'];
       }
     }
   }
diff --git a/core/modules/views_ui/views_ui.module b/core/modules/views_ui/views_ui.module
index 3960294..46adb0f 100644
--- a/core/modules/views_ui/views_ui.module
+++ b/core/modules/views_ui/views_ui.module
@@ -100,6 +100,7 @@ function views_ui_theme() {
     'views_ui_build_group_filter_form' => array(
       'render element' => 'form',
       'file' => 'views_ui.theme.inc',
+      'function' => 'theme_views_ui_build_group_filter_form',
     ),
 
     // On behalf of a plugin
diff --git a/core/themes/engines/twig/twig.engine b/core/themes/engines/twig/twig.engine
index c859b65..6311ada 100644
--- a/core/themes/engines/twig/twig.engine
+++ b/core/themes/engines/twig/twig.engine
@@ -38,23 +38,28 @@ function twig_init(Extension $theme) {
  * If the Twig debug setting is enabled, HTML comments including _theme() call
  * and template file name suggestions will surround the template markup.
  *
- * @param $template_file
+ * @param string $template_file
  *   The file name of the template to render.
- * @param $variables
+ * @param array $variables
  *   A keyed array of variables that will appear in the output.
  *
- * @return
+ * @return string
  *   The output generated by the template, plus any debug information.
  */
 function twig_render_template($template_file, $variables) {
   /** @var \Twig_Environment $twig_service */
   $twig_service = \Drupal::service('twig');
-  $output = array(
-    'debug_prefix'    => '',
-    'debug_info'      => '',
-    'rendered_markup' => $twig_service->loadTemplate($template_file)->render($variables),
-    'debug_suffix'    => '',
-  );
+  try {
+    $output = array(
+      'debug_prefix'    => '',
+      'debug_info'      => '',
+      'rendered_markup' => $twig_service->loadTemplate($template_file)->render($variables),
+      'debug_suffix'    => '',
+    );
+  }
+  catch (\Twig_Error_Loader $e) {
+    drupal_set_message($e->getMessage(), 'error');
+  }
   if ($twig_service->isDebug()) {
     $output['debug_prefix'] .= "\n\n<!-- THEME DEBUG -->";
     $output['debug_prefix'] .= "\n<!-- CALL: _theme('{$variables['theme_hook_original']}') -->";