Are 'Arrow Functions' and 'Functions' equivalent / interchangeable?

Arrow functions in ES2015 provide a more concise syntax.

• Can I replace all my function declarations / expressions with arrow functions now?
• What do I have to look out for?

Examples:

Constructor function

function User(name) {
  this.name = name;
}

// vs

const User = name => {
  this.name = name;
};

Prototype methods

User.prototype.getName = function() {
  return this.name;
};

// vs

User.prototype.getName = () => this.name;

Object (literal) methods

const obj = {
  getName: function() {
    // ...
  }
};

// vs

const obj = {
  getName: () => {
    // ...
  }
};

Callbacks

setTimeout(function() {
  // ...
}, 500);

// vs

setTimeout(() => {
  // ...
}, 500);

Variadic functions

function sum() {
  let args = [].slice.call(arguments);
  // ...
}

// vs
const sum = (...args) => {
  // ...
};