Async arrow functions look like this:

const foo = async () => {
  // do something
}

Async arrow functions look like this for a single argument passed to it:

const foo = async evt => {
  // do something with evt
}

Async arrow functions look like this for multiple arguments passed to it:

const foo = async (evt, callback) => {
  // do something with evt
  // return response with callback
}

The anonymous form works as well:

const foo = async function() {
  // do something
}

An async function declaration looks like this:

async function foo() {
  // do something
}

Using async function in a callback:

const foo = event.onCall(async () => {
  // do something
})

Using async method inside of a class:

async foo() {
  // do something
}

This the simplest way to assign an async arrow function expression to a named variable:

const foo = async () => {
  // do something
}

_{(Note that this is not strictly equivalent to async function foo() { }. Besides the differences between the function keyword and an arrow expression, the function in this answer is not "hoisted to the top".)}

Immediately Invoked Async Arrow Function:

(async () => {
    console.log(await asyncFunction());
})();

Immediately Invoked Async Function Expression:

(async function () {
    console.log(await asyncFunction());
})();