Both Chrome 57 and Firefox 52 now come with WebAssembly enabled, allowing developers to compile applications from C or C++ (and tentatively Rust) for the web. If you'd like to see what's possible, Mozilla has a few video available that explain and show off the platform.
For example, Unity's been building up support for wasm with its WebGL player, something it was forced to do when Chrome and other vendors started turning their backs on Flash and NPAPI (Netscape Plugin Application Programming Interface).
While you won't see a mass adoption in the near future, developers are now in a position to dedicate serious resources to WebAssembly. And, once other languages are supported, like C#, the floodgates will very much be open.