function alx_embed_html( $html ) {
    return '<div class="video-container">' . $html . '</div>';
}
add_filter( 'embed_oembed_html', 'alx_embed_html', 10, 3 );
add_filter( 'video_embed_html', 'alx_embed_html' ); // Jetpack

And next up, we need to add the CSS that makes it responsive to our style.css:

.video-container { 
  position: relative; 
  padding-bottom: 56.25%; 
  height: 0; 
  overflow: hidden; 
}

.video-container iframe, 
.video-container object, 
.video-container embed, 
.video-container video { 
  position: absolute; 
  top: 0; 
  left: 0; 
  width: 100%; 
  height: 100%; 
}