Add Video URL to Media Library

Is there any way to integrate YouTube or other videos from a URL with your Media Library? I want to do this so I can add videos from a URL and have them appear in the media library. That way, I can query the media library for recent videos to put on the front page or in a sidebar.

If this is not possible, is there another way to post my most recent videos on the front page of my blog?

From this page, it looks like WordPress.com blogs have this functionality built it. https://support.wordpress.com/videos/youtube/

Is there a plugin or any other way to get this functionality on self hosted WP blogs?

Thanks,
Jeff