Since 1996, HTML standards have been maintained by the World Wide Web Consortium (W3C) with input from commercial software vendors.
As from 2008, the HTML5 web standards are currently being developed by the Web Hypertext Application Technology Working Group (WHATWG) and the World Wide Web Consortium (W3C).
I also found this HTML5 browser comparison chart which is the best place to find out the latest support for HTML5 in browsers:
Whencaniuse.com also provides a detailed overview of what html5 elements are supported in every version of browser. It also includes a comparison chart.