With no overlay
With Custom Overlay (youtube)
Vimeo (More options to control the play button/details of the vimeo video can be set on the vimeo video itself. On Vimeo.com)
With Custom Overlay (Vimeo)

Full width Video Overlay  (on click goes to youtube player still maintaining width)

 

That Play Button in the bottom Right

In creates a video in a Modal from Youtube!

This is a video pulled from a CDN such as AWS

It will always cover the background but takes a little bit more work to set up. No Audio Though