I tried to give an overview on the technical details of the HTML5 MSE/EME, which is used e.g. by Netflix and Youtube. If you are interested in any details, just post it here, happy to answer.
on the commercial prodcut side, the bitmovin player https://bitmovin.com/player/ is best one covering HLS & DASH on all browsers. There are also a lot of demos at http://www.dash-player.com/demo/
Why isn't this built into the browser?