diff --git a/wp-includes/post-template.php b/wp-includes/post-template.php
index 8219b27f69..4c0fed2b90 100644
--- a/wp-includes/post-template.php
+++ b/wp-includes/post-template.php
@@ -760,6 +760,10 @@ function get_body_class( $class = '' ) {
 		$classes[] = 'wp-custom-logo';
 	}
 
+	if ( current_theme_supports( 'responsive-embeds' ) ) {
+		$classes[] = 'wp-embed-responsive';
+	}
+
 	$page = $wp_query->get( 'page' );
 
 	if ( ! $page || $page < 2 ) {
diff --git a/wp-includes/rest-api/endpoints/class-wp-rest-themes-controller.php b/wp-includes/rest-api/endpoints/class-wp-rest-themes-controller.php
index 4aa7db4f6f..dbfaa839cb 100644
--- a/wp-includes/rest-api/endpoints/class-wp-rest-themes-controller.php
+++ b/wp-includes/rest-api/endpoints/class-wp-rest-themes-controller.php
@@ -111,8 +111,9 @@ class WP_REST_Themes_Controller extends WP_REST_Controller {
 			$formats                           = array_merge( array( 'standard' ), $formats );
 			$data['theme_supports']['formats'] = $formats;
 
-			$data['theme_supports']['post-thumbnails'] = false;
-			$post_thumbnails                           = get_theme_support( 'post-thumbnails' );
+			$data['theme_supports']['post-thumbnails']   = false;
+			$data['theme_supports']['responsive-embeds'] = (bool) get_theme_support( 'responsive-embeds' );
+			$post_thumbnails                             = get_theme_support( 'post-thumbnails' );
 
 			if ( $post_thumbnails ) {
 				// $post_thumbnails can contain a nested array of post types.
@@ -156,16 +157,21 @@ class WP_REST_Themes_Controller extends WP_REST_Controller {
 					'type'        => 'array',
 					'readonly'    => true,
 					'properties'  => array(
-						'formats'         => array(
+						'formats'           => array(
 							'description' => __( 'Post formats supported.' ),
 							'type'        => 'array',
 							'readonly'    => true,
 						),
-						'post-thumbnails' => array(
+						'post-thumbnails'   => array(
 							'description' => __( 'Whether the theme supports post thumbnails.' ),
 							'type'        => array( 'array', 'bool' ),
 							'readonly'    => true,
 						),
+						'responsive-embeds' => array(
+							'description' => __( 'Whether the theme supports responsive embedded content.' ),
+							'type'        => 'bool',
+							'readonly'    => true,
+						),
 					),
 				),
 			),
diff --git a/wp-includes/theme.php b/wp-includes/theme.php
index 3d26800436..ee84c031f4 100644
--- a/wp-includes/theme.php
+++ b/wp-includes/theme.php
@@ -2318,12 +2318,14 @@ function get_theme_starter_content() {
  * @since 4.1.0 The `title-tag` feature was added
  * @since 4.5.0 The `customize-selective-refresh-widgets` feature was added
  * @since 4.7.0 The `starter-content` feature was added
+ * @since 5.0.0 The `responsive-embeds` feature was added.
  *
  * @global array $_wp_theme_features
  *
  * @param string $feature  The feature being added. Likely core values include 'post-formats',
  *                         'post-thumbnails', 'html5', 'custom-logo', 'custom-header-uploads',
- *                         'custom-header', 'custom-background', 'title-tag', 'starter-content', etc.
+ *                         'custom-header', 'custom-background', 'title-tag', 'starter-content',
+ *                         'responsive-embeds', etc.
  * @param mixed  $args,... Optional extra arguments to pass along with certain features.
  * @return void|bool False on failure, void otherwise.
  */
diff --git a/wp-includes/version.php b/wp-includes/version.php
index 56090f2a0f..290e1612d6 100644
--- a/wp-includes/version.php
+++ b/wp-includes/version.php
@@ -13,7 +13,7 @@
  *
  * @global string $wp_version
  */
-$wp_version = '5.1-alpha-44137';
+$wp_version = '5.1-alpha-44138';
 
 /**
  * Holds the WordPress DB revision, increments when changes are made to the WordPress DB schema.