diff --git a/core/modules/update/update.manager.inc b/core/modules/update/update.manager.inc
index 6b6767b..04804c7 100644
--- a/core/modules/update/update.manager.inc
+++ b/core/modules/update/update.manager.inc
@@ -257,8 +257,13 @@ function update_manager_update_form($form, $form_state = array(), $context) {
   if (!empty($projects['manual'])) {
     $prefix = '<h2>' . t('Manual updates required') . '</h2>';
     $prefix .= '<p>' . t('Updates of Drupal core are not supported at this time.') . '</p>';
+    $table = array(
+      '#theme' => 'table',
+      '#header' => $headers,
+      '#rows' => $projects['manual'],
+    );
     $form['manual_updates'] = array(
-      '#markup' => theme('table', array('header' => $headers, 'rows' => $projects['manual'])),
+      '#markup' => drupal_render($table),
       '#prefix' => $prefix,
       '#weight' => 120,
     );
@@ -279,7 +284,11 @@ function update_manager_update_form($form, $form_state = array(), $context) {
 function theme_update_manager_update_form($variables) {
   $form = $variables['form'];
   $last = Drupal::state()->get('update.last_check') ?: 0;
-  $output = theme('update_last_check', array('last' => $last));
+  $update_last_check = array(
+    '#theme' => 'update_last_check',
+    '#last' => $last,
+  );
+  $output = drupal_render($update_last_check);
   $output .= drupal_render_children($form);
   return $output;
 }
@@ -347,11 +356,12 @@ function update_manager_update_form_submit($form, &$form_state) {
  */
 function update_manager_download_batch_finished($success, $results) {
   if (!empty($results['errors'])) {
-    $error_list = array(
-      'title' => t('Downloading updates failed:'),
-      'items' => $results['errors'],
+    $item_list = array(
+      '#theme' => 'item_list',
+      '#title' => t('Downloading updates failed:'),
+      '#items' => $results['errors'],
     );
-    drupal_set_message(theme('item_list', $error_list), 'error');
+    drupal_set_message(drupal_render($item_list), 'error');
   }
   elseif ($success) {
     drupal_set_message(t('Updates downloaded successfully.'));
diff --git a/core/modules/update/update.report.inc b/core/modules/update/update.report.inc
index d21a5cb..50a9da6 100644
--- a/core/modules/update/update.report.inc
+++ b/core/modules/update/update.report.inc
@@ -18,7 +18,11 @@ function theme_update_report($variables) {
   $data = $variables['data'];
 
   $last = Drupal::state()->get('update.last_check') ?: 0;
-  $output = theme('update_last_check', array('last' => $last));
+  $update_last_check = array(
+    '#theme' => 'update_last_check',
+    '#last' => $last,
+  );
+  $output = drupal_render($update_last_check);
 
   if (!is_array($data)) {
     $output .= '<p>' . $data . '</p>';
@@ -43,32 +47,46 @@ function theme_update_report($variables) {
     switch ($project['status']) {
       case UPDATE_CURRENT:
         $class = 'ok';
-        $icon = theme('image', array('uri' => 'core/misc/watchdog-ok.png', 'width' => 18, 'height' => 18, 'alt' => t('ok'), 'title' => t('ok')));
+        $uri = 'core/misc/watchdog-ok.png';
+        $text = t('ok');
         break;
       case UPDATE_UNKNOWN:
       case UPDATE_FETCH_PENDING:
       case UPDATE_NOT_FETCHED:
         $class = 'unknown';
-        $icon = theme('image', array('uri' => 'core/misc/watchdog-warning.png', 'width' => 18, 'height' => 18, 'alt' => t('warning'), 'title' => t('warning')));
+        $uri = 'core/misc/watchdog-warning.png';
+        $text = t('warning');
         break;
       case UPDATE_NOT_SECURE:
       case UPDATE_REVOKED:
       case UPDATE_NOT_SUPPORTED:
         $class = 'error';
-        $icon = theme('image', array('uri' => 'core/misc/watchdog-error.png', 'width' => 18, 'height' => 18, 'alt' => t('error'), 'title' => t('error')));
+        $uri = 'core/misc/watchdog-error.png';
+        $text = t('error');
         break;
       case UPDATE_NOT_CHECKED:
       case UPDATE_NOT_CURRENT:
       default:
         $class = 'warning';
-        $icon = theme('image', array('uri' => 'core/misc/watchdog-warning.png', 'width' => 18, 'height' => 18, 'alt' => t('warning'), 'title' => t('warning')));
+        $uri = 'core/misc/watchdog-warning.png';
+        $text = t('warning');
         break;
     }
 
+    $icon = array(
+      '#theme' => 'image',
+      '#width' => 18,
+      '#height' => 18,
+      '#uri' => $uri,
+      '#alt' => $text,
+      '#title' => $text,
+    );
+
     $row = '<div class="version-status">';
-    $status_label = theme('update_status_label', array('status' => $project['status']));
+    $update_status_label = array('#theme' => 'update_status_label', '#status' => $project['status']);
+    $status_label = drupal_render($update_status_label);
     $row .= !empty($status_label) ? $status_label : check_plain($project['reason']);
-    $row .= '<span class="icon">' . $icon . '</span>';
+    $row .= '<span class="icon">' . drupal_render($icon) . '</span>';
     $row .= "</div>\n";
 
     $row .= '<div class="project">';
@@ -118,32 +136,62 @@ function theme_update_report($variables) {
               ) {
             $version_class[] = 'version-recommended-strong';
           }
-          $versions_inner .= theme('update_version', array('version' => $project['releases'][$project['recommended']], 'tag' => t('Recommended version:'), 'class' => $version_class));
+          $update_version = array(
+            '#theme' => 'update_version',
+            '#version' => $project['releases'][$project['recommended']],
+            '#tag' => t('Recommended version:'),
+            '#class' => $version_class,
+          );
+          $versions_inner .= drupal_render($update_version);
         }
 
         // Now, print any security updates.
         if (!empty($project['security updates'])) {
           $security_class[] = 'version-security';
           foreach ($project['security updates'] as $security_update) {
-            $versions_inner .= theme('update_version', array('version' => $security_update, 'tag' => t('Security update:'), 'class' => $security_class));
+            $update_version = array(
+              '#theme' => 'update_version',
+              '#version' => $security_update,
+              '#tag' => t('Security update:'),
+              '#class' => $security_class,
+            );
+            $versions_inner .= drupal_render($update_version);
           }
         }
       }
 
       if ($project['recommended'] !== $project['latest_version']) {
-        $versions_inner .= theme('update_version', array('version' => $project['releases'][$project['latest_version']], 'tag' => t('Latest version:'), 'class' => array('version-latest')));
+        $update_version = array(
+          '#theme' => 'update_version',
+          '#version' => $project['releases'][$project['latest_version']],
+          '#tag' => t('Latest version:'),
+          '#class' => array('version-latest'),
+        );
+        $versions_inner .= drupal_render($update_version);
       }
       if ($project['install_type'] == 'dev'
           && $project['status'] != UPDATE_CURRENT
           && isset($project['dev_version'])
           && $project['recommended'] !== $project['dev_version']) {
-        $versions_inner .= theme('update_version', array('version' => $project['releases'][$project['dev_version']], 'tag' => t('Development version:'), 'class' => array('version-latest')));
+        $update_version = array(
+          '#theme' => 'update_version',
+          '#version' => $project['releases'][$project['dev_version']],
+          '#tag' => t('Development version:'),
+          '#class' => array('version-latest'),
+        );
+        $versions_inner .= drupal_render($update_version);
       }
     }
 
     if (isset($project['also'])) {
       foreach ($project['also'] as $also) {
-        $versions_inner .= theme('update_version', array('version' => $project['releases'][$also], 'tag' => t('Also available:'), 'class' => array('version-also-available')));
+        $update_version = array(
+          '#theme' => 'update_version',
+          '#version' => $project['releases'][$also],
+          '#tag' => t('Also available:'),
+          '#class' => array('version-also-available'),
+        );
+        $versions_inner .= drupal_render($update_version);
       }
     }
 
@@ -171,7 +219,11 @@ function theme_update_report($variables) {
       $row .= t('Includes:');
       $includes_items[] = t('Enabled: %includes', array('%includes' => implode(', ', $project['includes'])));
       $includes_items[] = t('Disabled: %disabled', array('%disabled' => implode(', ', $project['disabled'])));
-      $row .= theme('item_list', array('items' => $includes_items));
+      $item_list = array(
+        '#theme' => 'item_list',
+        '#items' => $includes_items,
+      );
+      $row .= drupal_render($item_list);
     }
     else {
       $row .= t('Includes: %includes', array('%includes' => implode(', ', $project['includes'])));
@@ -183,11 +235,15 @@ function theme_update_report($variables) {
       asort($project['base_themes']);
       $base_themes = array();
       foreach ($project['base_themes'] as $base_key => $base_theme) {
+        $update_status_label = array(
+          '#theme' => 'update_status_label',
+          '#status' => $status[$base_key],
+        );
         switch ($status[$base_key]) {
           case UPDATE_NOT_SECURE:
           case UPDATE_REVOKED:
           case UPDATE_NOT_SUPPORTED:
-            $base_themes[] = t('%base_theme (!base_label)', array('%base_theme' => $base_theme, '!base_label' => theme('update_status_label', array('status' => $status[$base_key]))));
+            $base_themes[] = t('%base_theme (!base_label)', array('%base_theme' => $base_theme, '!base_label' => drupal_render($update_status_label)));
             break;
 
           default:
@@ -228,7 +284,15 @@ function theme_update_report($variables) {
     if (!empty($rows[$type_name])) {
       ksort($rows[$type_name]);
       $output .= "\n<h3>" . $type_label . "</h3>\n";
-      $output .= theme('table', array('header' => $header, 'rows' => $rows[$type_name], 'attributes' => array('class' => array('update'))));
+      $table = array(
+        '#theme' => 'table',
+        '#header' => $header,
+        '#rows' => $rows[$type_name],
+        '#attributes' => array(
+          'class' => array('update'),
+        ),
+      );
+      $output .= drupal_render($table);
     }
   }
   drupal_add_css(drupal_get_path('module', 'update') . '/css/update.admin.css');
@@ -303,7 +367,11 @@ function theme_update_version($variables) {
     'title' => t('Release notes'),
     'href' => $version['release_link'],
   );
-  $output .= theme('links__update_version', array('links' => $links));
+  $links__update_version = array(
+    '#theme' => 'links__update_version',
+    '#links' => $links,
+  );
+  $output .= drupal_render($links__update_version);
   $output .= '</td>';
   $output .= '</tr>';
   $output .= "</table>\n";