Unity WebGL content is supported in the current versions of most major browsers on the desktop, however there are differences in the level of support offered by the different browsers. Mobile devices are not supported by Unity WebGL.
Not all features of Unity are available in WebGL builds, mostly due to constraints of the platform. Specifically:
System.Threading namespace is not supported.
WebGL builds cannot be debugged in MonoDevelop or Visual Studio. See: Debugging and trouble shooting WebGL builds.
Browsers do not allow direct access to IP sockets for networking, due to security concerns. See: WebGL Networking.
The WebGL graphics API is equivalent to OpenGL ES 2.0, which has some limitations. See: WebGL Graphics.
WebGL builds use a custom backend for Audio, based on the Web Audio API. This supports only basic audio functionality. See: Using Audio in WebGL.
WebGL is an AOT platform, so it does not allow dynamic generation of code using
System.Reflection.Emit. This is the same on all other IL2CPP platforms, iOS, and most consoles.