Acording to WebKit sources, the company has achieved 100 percent ES6 compatibility on the Kangax Compatibility Table, which is the first milestone. Based on Apple's Safrai web browser, Safari Technical Preview 4, which was recently released has itself reached 99% compatibility.
In other exciting development, the V8 team has integrated async/await. Even though Microsoft was first to release a browser preview with async/await, V8's consumption in Node.js given it a wider perspective. As a developer, you can make use of async/await in the code provided if you are using a transpiler like TypeScript. However, a native implementation of V8 will eliminate the need for an intermediate tool like TypeScript.
Recently, Microsoft has updated their Microsoft Edge preview browser with ES6 modules, which enable the browser to work well considering the static nature of the modules. The Edge preview also comes with proposed ES2016 features. Microsoft is the first to implement ES7 modules. WebKit not yet implemented the modules.
WebKit revealed that this particular feature is not in their roadmap list because it's difficult to test them in an automatic manner and the spec is still not finalized.
We are not sure whether these new features and advancements will be integrated in the public release. It all depend upon the feedback from developers and customers.