HTML5 video
Support for HTML5 video has been steadily increasing. In June 2013, Netflix added support for HTML5 video. In January 2015, YouTube switched to using HTML5 video instead of Flash by default. In December 2015, Facebook switched from Flash to HTML5 for all video content.
Adobe Flash
Representing open standards, inventor of CSS and co-author of HTML5, Håkon Wium Lie explained in a Google tech talk of 2007, entitled "the  element", the proposal of Theora as the format for HTML5 video:
I believe very strongly, that we need to agree on some kind of baseline video format if [the video element] is going to succeed. Flash is today the baseline format on the web. The problem with Flash is that it's not an open standard.