diff --git a/core/modules/filter/filter.admin.inc b/core/modules/filter/filter.admin.inc
index 806c1d7..48ee96c 100644
--- a/core/modules/filter/filter.admin.inc
+++ b/core/modules/filter/filter.admin.inc
@@ -236,15 +236,19 @@ function filter_admin_format_form($form, &$form_state, $format) {
 
   // Filter order (tabledrag).
   $form['filters']['order'] = array(
-    '#type' => 'item',
+    '#type' => 'table',
+    // For filter.admin.js
+    '#attributes' => array('id' => 'filter-order'),
     '#title' => t('Filter processing order'),
-    '#theme' => 'filter_admin_format_filter_order',
-    // This item is used as a pure wrapping container with heading. Ignore its
-    // value, since 'filters' should only contain filter definitions.
-    // @see http://drupal.org/node/1829202
-    '#input' => FALSE,
+    '#tabledrag' => array(
+      array('order', 'sibling', 'filter-order-weight'),
+    ),
+    '#tree' => FALSE,
+    '#theme_wrappers' => array('form_element'),
   );
   foreach ($filter_info as $name => $filter) {
+    $form['filters']['order'][$name]['#attributes']['class'][] = 'draggable';
+    $form['filters']['order'][$name]['#weight'] = $filters[$name]->weight;
     $form['filters']['order'][$name]['filter'] = array(
       '#markup' => $filter['title'],
     );
@@ -255,9 +259,12 @@ function filter_admin_format_form($form, &$form_state, $format) {
       '#delta' => 50,
       '#default_value' => $filters[$name]->weight,
       '#parents' => array('filters', $name, 'weight'),
+      '#attributes' => array('class' => array('filter-order-weight')),
     );
-    $form['filters']['order'][$name]['#weight'] = $filters[$name]->weight;
   }
+  // Make sure filters are in the correct order, since filter_get_filters()
+  // doesn't return sorted filters.
+  uasort($form['filters']['order'], 'element_sort');
 
   // Filter settings.
   $form['filter_settings'] = array(
@@ -291,37 +298,6 @@ function filter_admin_format_form($form, &$form_state, $format) {
 }
 
 /**
- * Returns HTML for a text format's filter order form.
- *
- * @param array $variables
- *   An associative array containing:
- *   - element: A render element representing the form.
- *
- * @ingroup themeable
- */
-function theme_filter_admin_format_filter_order($variables) {
-  $element = $variables['element'];
-
-  // Filter order (tabledrag).
-  $rows = array();
-  foreach (element_children($element, TRUE) as $name) {
-    $element[$name]['weight']['#attributes']['class'][] = 'filter-order-weight';
-    $rows[] = array(
-      'data' => array(
-        drupal_render($element[$name]['filter']),
-        drupal_render($element[$name]['weight']),
-      ),
-      'class' => array('draggable'),
-    );
-  }
-  $output = drupal_render_children($element);
-  $output .= theme('table', array('rows' => $rows, 'attributes' => array('id' => 'filter-order')));
-  drupal_add_tabledrag('filter-order', 'order', 'sibling', 'filter-order-weight', NULL, NULL, TRUE);
-
-  return $output;
-}
-
-/**
  * Form validation handler for filter_admin_format_form().
  *
  * @see filter_admin_format_form_submit()
diff --git a/core/modules/filter/filter.admin.js b/core/modules/filter/filter.admin.js
index f55159a..123576a 100644
--- a/core/modules/filter/filter.admin.js
+++ b/core/modules/filter/filter.admin.js
@@ -33,7 +33,7 @@ Drupal.behaviors.filterStatus = {
           }
         }
         // Restripe table after toggling visibility of table row.
-        Drupal.tableDrag['filter-order'].restripeTable();
+        Drupal.tableDrag['edit-filters-order'].restripeTable();
       });
 
       // Attach summary for configurable filters (only for screen-readers).
diff --git a/core/modules/filter/filter.module b/core/modules/filter/filter.module
index 725d931..5345335 100644
--- a/core/modules/filter/filter.module
+++ b/core/modules/filter/filter.module
@@ -74,22 +74,18 @@ function filter_help($path, $arg) {
  */
 function filter_theme() {
   return array(
-    'filter_admin_format_filter_order' => array(
-      'render element' => 'element',
-      'file' => 'filter.admin.inc',
-    ),
     'filter_tips' => array(
       'variables' => array('tips' => NULL, 'long' => FALSE),
       'file' => 'filter.pages.inc',
+      'template' => 'filter-tips',
     ),
     'text_format_wrapper' => array(
       'render element' => 'element',
-    ),
-    'filter_tips_more_info' => array(
-      'variables' => array(),
+      'template' => 'text-format-wrapper',
     ),
     'filter_guidelines' => array(
       'variables' => array('format' => NULL),
+      'template' => 'filter-guidelines',
     ),
     'filter_html_image_secure_image' => array(
       'variables' => array('image' => NULL),
@@ -919,11 +915,23 @@ function filter_process_format($element) {
     '#parents' => array_merge($element['#parents'], array('format')),
   );
 
+  $filter_tips_link = array(
+    '#theme' => 'link',
+    '#text' => t('More information about text formats'),
+    '#path' => 'filter/tips',
+    '#options' => array(
+        'attributes' => array('target' => '_blank'),
+        'html' => FALSE,
+    ),
+    '#prefix' => '<p>',
+    '#suffix' => '</p>',
+  );
+
   $element['format']['help'] = array(
     '#type' => 'container',
-    '#theme' => 'filter_tips_more_info',
     '#attributes' => array('class' => array('filter-help')),
     '#weight' => 0,
+    $filter_tips_link,
   );
 
   $all_formats = filter_formats();
@@ -989,24 +997,20 @@ function filter_form_access_denied($element) {
 }
 
 /**
- * Returns HTML for a text format-enabled form element.
+ * Prepares variables for the text-format-wrapper template.
+ *
+ * Default template: text-format-wrapper.html.twig.
  *
  * @param array $variables
  *   An associative array containing:
  *   - element: A render element containing #children and #description.
- *
- * @ingroup themeable
  */
-function theme_text_format_wrapper($variables) {
+function template_preprocess_text_format_wrapper(&$variables) {
   $element = $variables['element'];
-  $output = '<div class="text-format-wrapper form-item">';
-  $output .= $element['#children'];
+  $variables['children'] = $element['#children'];
   if (!empty($element['#description'])) {
-    $output .= '<div class="description">' . $element['#description'] . '</div>';
+    $variables['description'] = $element['#description'];
   }
-  $output .= "</div>\n";
-
-  return $output;
 }
 
 /**
@@ -1180,32 +1184,79 @@ function filter_dom_serialize_escape_cdata_element($dom_document, $dom_element,
 }
 
 /**
- * Returns HTML for a link to the more extensive filter tips.
+ * Prepares variables for guidelines for a text format.
+ *
+ * Default template: filter-guidelines.html.twig.
  *
- * @ingroup themeable
+ * @param array $variables
+ *   An associative array containing:
+ *   - format: An object representing a text format.
  */
-function theme_filter_tips_more_info() {
-  return '<p>' . l(t('More information about text formats'), 'filter/tips', array('attributes' => array('target' => '_blank'))) . '</p>';
+function template_preprocess_filter_guidelines(&$variables) {
+  $format = $variables['format'];
+  $variables['attributes']['class'][] = 'filter-guidelines-item';
+  $variables['attributes']['class'][] = 'filter-guidelines-' . $format->format;
+  $variables['tips'] = array(
+    '#theme' => 'filter_tips',
+    '#tips' => _filter_tips($format->format, FALSE),
+  );
 }
 
 /**
- * Returns HTML for guidelines for a text format.
+ * Prepares variables for a set of filter tips
+ *
+ * Default template: filter-tips.html.twig.
  *
  * @param array $variables
  *   An associative array containing:
- *   - format: An object representing a text format.
- *
- * @ingroup themeable
- */
-function theme_filter_guidelines($variables) {
-  $format = $variables['format'];
-  $attributes['class'][] = 'filter-guidelines-item';
-  $attributes['class'][] = 'filter-guidelines-' . $format->format;
-  $output = '<div' . new Attribute($attributes) . '>';
-  $output .= '<h4 class="label">' . check_plain($format->name) . '</h4>';
-  $output .= theme('filter_tips', array('tips' => _filter_tips($format->format, FALSE)));
-  $output .= '</div>';
-  return $output;
+ *   - tips: An array containing descriptions and a CSS ID in the form of
+ *     'module-name/filter-id' (only used when $long is TRUE) for each
+ *     filter in one or more text formats. Example:
+ *     @code
+ *       array(
+ *         'Full HTML' => array(
+ *           0 => array(
+ *             'tip' => 'Web page addresses and e-mail addresses turn into links automatically.',
+ *             'id' => 'filter/2',
+ *           ),
+ *         ),
+ *       );
+ *     @endcode
+ *   - long: (optional) Whether the passed-in filter tips contain extended
+ *     explanations, i.e. intended to be output on the path 'filter/tips'
+ *     (TRUE), or are in a short format, i.e. suitable to be displayed below a
+ *     form element. Defaults to FALSE.
+ */
+function template_preprocess_filter_tips(&$variables) {
+  $tips = $variables['tips'];
+  $long = $variables['long'];
+  $output = '';
+
+  $multiple = count($tips) > 1;
+
+  foreach ($variables['tips'] as $name => $tiplist) {
+    foreach ($tiplist as $tip_key => $tip) {
+      $tiplist[$tip_key]['attributes'] = new Attribute(array());
+      if ($long) {
+        $tiplist[$tip_key]['attributes']['class'] =  array('filter-' . str_replace("/", "-", $tip['id']));
+      }
+    }
+
+    $attributes = array(
+      'class' => array(
+        'filter-type',
+        'filter-' . drupal_html_class($name),
+      ),
+    );
+
+    $variables['tips'][$name] = array(
+      'attributes' => new Attribute($attributes),
+      'name' => check_plain($name),
+      'list' => $tiplist,
+    );
+  }
+
+  $variables['multiple'] = $multiple;
 }
 
 /**
@@ -1818,18 +1869,15 @@ function _filter_html_image_secure_process($text) {
 }
 
 /**
- * Formats an image DOM element that has an invalid source.
- *
- * @param DOMElement $image
- *   An IMG node to format, parsed from the filtered text.
+ * Prepares variables for Formats an image DOM element that has an invalid source.
  *
- * @return void
- *   Unlike other theme functions, the passed in $image is altered by reference.
+ * @param array $variables
+ *   An associative array containing:
+ *   - image: A DOMElement IMG node to format, parsed from the filtered text.
  *
  * @see _filter_html_image_secure_process()
- * @ingroup themeable
  */
-function theme_filter_html_image_secure_image(&$variables) {
+function template_preprocess_filter_html_image_secure_image(&$variables) {
   $image = $variables['image'];
 
   // Turn an invalid image into an error indicator.
diff --git a/core/modules/filter/filter.pages.inc b/core/modules/filter/filter.pages.inc
index 5b20d4f..f0ac5d6 100644
--- a/core/modules/filter/filter.pages.inc
+++ b/core/modules/filter/filter.pages.inc
@@ -19,76 +19,18 @@
  */
 function filter_tips_long($format = NULL) {
   if (!empty($format)) {
-    $output = theme('filter_tips', array('tips' => _filter_tips($format->format, TRUE), 'long' => TRUE));
+    $filter_tips = array(
+      '#theme' => 'filter_tips',
+      '#tips' => _filter_tips($format->format, TRUE),
+      '#long' => TRUE,
+    );
   }
   else {
-    $output = theme('filter_tips', array('tips' => _filter_tips(-1, TRUE), 'long' => TRUE));
+    $filter_tips = array(
+      '#theme' => 'filter_tips',
+      '#tips' => _filter_tips(-1, TRUE),
+      '#long' => TRUE,
+    );
   }
-  return $output;
-}
-
-/**
- * Returns HTML for a set of filter tips.
- *
- * @param array $variables
- *   An associative array containing:
- *   - tips: An array containing descriptions and a CSS ID in the form of
- *     'module-name/filter-id' (only used when $long is TRUE) for each
- *     filter in one or more text formats. Example:
- *     @code
- *       array(
- *         'Full HTML' => array(
- *           0 => array(
- *             'tip' => 'Web page addresses and e-mail addresses turn into links automatically.',
- *             'id' => 'filter/2',
- *           ),
- *         ),
- *       );
- *     @endcode
- *   - long: (optional) Whether the passed-in filter tips contain extended
- *     explanations, i.e. intended to be output on the path 'filter/tips'
- *     (TRUE), or are in a short format, i.e. suitable to be displayed below a
- *     form element. Defaults to FALSE.
- *
- * @see _filter_tips()
- * @ingroup themeable
- */
-function theme_filter_tips($variables) {
-  $tips = $variables['tips'];
-  $long = $variables['long'];
-  $output = '';
-
-  $multiple = count($tips) > 1;
-  if ($multiple) {
-    $output = '<h2>' . t('Text Formats') . '</h2>';
-  }
-
-  if (count($tips)) {
-    if ($multiple) {
-      $output .= '<div class="compose-tips">';
-    }
-    foreach ($tips as $name => $tiplist) {
-      if ($multiple) {
-        $output .= '<div class="filter-type filter-' . drupal_html_class($name) . '">';
-        $output .= '<h3>' . $name . '</h3>';
-      }
-
-      if (count($tiplist) > 0) {
-        $output .= '<ul class="tips">';
-        foreach ($tiplist as $tip) {
-          $output .= '<li' . ($long ? ' class="filter-' . str_replace("/", "-", $tip['id']) . '">' : '>') . $tip['tip'] . '</li>';
-        }
-        $output .= '</ul>';
-      }
-
-      if ($multiple) {
-        $output .= '</div>';
-      }
-    }
-    if ($multiple) {
-      $output .= '</div>';
-    }
-  }
-
-  return $output;
+  return $filter_tips;
 }
diff --git a/core/modules/filter/templates/filter-guidelines.html.twig b/core/modules/filter/templates/filter-guidelines.html.twig
new file mode 100644
index 0000000..c028aaa
--- /dev/null
+++ b/core/modules/filter/templates/filter-guidelines.html.twig
@@ -0,0 +1,24 @@
+{#
+/**
+ * @file
+ * Default theme implementation for guidelines for a text format.
+ *
+ * Available variables:
+ * - format: An object representing a text format.
+ * - attributes: Remaining html attributes for the containing element.
+ * - tips: Descriptions and a CSS id in the form of 'module-name/filter-id'
+ *   (only used when $long is TRUE) for each filter in one or more text
+ *   formats.
+ *
+ * @todo Remove striptags when auto_escape is resolved http://drupal.org/node/1712444.
+ *
+ * @see template_preprocess()
+ * @see template_preprocess_filter_tips()
+ *
+ * @ingroup themeable
+ */
+ #}
+<div{{ attributes }}>
+  <h4 class="label">{{ format.name|striptags }}</h4>
+  {{ tips }}
+</div>
diff --git a/core/modules/filter/templates/filter-tips.html.twig b/core/modules/filter/templates/filter-tips.html.twig
new file mode 100644
index 0000000..367730a
--- /dev/null
+++ b/core/modules/filter/templates/filter-tips.html.twig
@@ -0,0 +1,55 @@
+{#
+/**
+ * @file
+ * Default theme implementation for a set of filter tips.
+ *
+ * Available variables:
+ * - tips: Descriptions and a CSS id in the form of 'module-name/filter-id'
+ *   (only used when $long is TRUE) for each filter in one or more text
+ *   formats.
+ * - long: (optional) Whether the passed-in filter tips contain extended
+ *   explanations, i.e. intended to be output on the path 'filter/tips'
+ *   (TRUE), or are in a short format, i.e. suitable to be displayed below a
+ *   form element. Defaults to FALSE.
+ *
+ * @todo reimplement once http://drupal.org/node/1778624 gets resolved.
+ *
+ * @see template_preprocess()
+ * @see template_preprocess_filter_tips()
+ *
+ * @ingroup themeable
+ */
+#}
+{% if multiple %}
+  <h2>{{ 'Text Formats'|t }}</h2>
+{% endif %}
+
+{% if tips|length %}
+  {% if multiple %}
+    <div class="compose-tips">
+  {% endif %}
+
+  {% for tip in tips %}
+    {% if multiple %}
+     <div{{ tip.attributes }}>
+      <h3>{{ tip.name }}</h3>
+    {% endif %}
+
+    {% if tip.list|length %}
+      <ul class="tips">
+      {% for item in tip.list %}
+        {# Only set the class if the type is long #}
+        <li{{ item.attributes }}>{{ item.tip }}</li>
+      {% endfor %}
+      </ul>
+    {% endif %}
+
+    {% if multiple %}
+      </div>
+    {% endif %}
+  {% endfor %}
+
+  {% if multiple %}
+    </div>
+  {% endif %}
+{% endif %}
diff --git a/core/modules/filter/templates/text-format-wrapper.html.twig b/core/modules/filter/templates/text-format-wrapper.html.twig
new file mode 100644
index 0000000..013d899
--- /dev/null
+++ b/core/modules/filter/templates/text-format-wrapper.html.twig
@@ -0,0 +1,22 @@
+{#
+/**
+ * @file
+ * Default theme implementation for a text format-enabled form element.
+ *
+ * Available variables:
+ * - children: Text format element children.
+ * - description: Text format element description.
+ *
+ * @see template_preprocess()
+ * @see template_preprocess_text_format_wrapper()
+ *
+ * @ingroup themeable
+ */
+#}
+<div class="text-format-wrapper">
+  {{ children }}
+  {% if description %}
+    <div class="description">{{ description }}</div>
+  {% endif %}
+</div>
+