Modules are not yet natively supported in any browser. You will need to use a transpiler such as Traceur or Babel. Take a look at one of the following to help you get started:
- Choose ES6 modules Today!
- ES6 In Depth: Using ES6 today with Babel and Broccoli
- Writing client-side ES6 with webpack
As for classes, you may be able to use these natively without having to go through a transpiler. You can check the compatibility table here to see which browsers support classes natively today:
https://kangax.github.io/compat-table/es6/
As of right now, you can see that the majority of browsers do not yet support classes natively. However, if you are using Babel or Traceur, that shouldn’t be a concern.