In the past browser compatibility caused big headaches for web developers but things are looking up as now even Microsoft is focusing on the future. With the arrival of the Edge browser in Windows 10, the software giant will not only drop legacy IE support but will also do its best to support web standards and make the Edge rendering engine as identical to WebKit as possible:
As part of that effort, Edge now supports 45 new web standards, and has received thousands of fixes to make sure it renders content correctly. Perhaps nothing signifies Microsoft's new approach more than this statement: “Any Edge-WebKit differences [in rendering] are bugs that we're interested in fixing”. That's a huge departure for a company that until very recently was only focused on its own product and standards.
And just to drive that point home, Edge now mimics a ton of WebKit functionality: from the User Agent String to supporting WebKit-prefixed CSS, to relaxing rules on standards and being much more forgiving when it comes to malformed code. All of these changes both big and small result in a much better experience for the end-user.
WebKit (and forks of it) is the most widely used web rendering engine, it's used by Safari and Chrome