Babel and the latest JavaScript syntax

We've been building up this application to act as our base and in the process we've introduced a lot of syntax that may not be the same JavaScript that you're used to writing! For example, we've written a few functions with this sort of syntax:

const foo = () => {
  doSomething();
  doSomethingElse();
}

The syntax here is not particularly tricky and you can probably figure out what's going on, but maybe you don't fully understand how all of that ends up as a function when all is said and done. You may be more used to writing functions in a similar pattern to the following:

var foo = function() {
  doSomething();
  doSomethingElse();
}

Or maybe something more like a function declaration without the variable, such as the following function:

function foo() {
  doSomething();
  doSomethingElse();
}

The reality is that...