What you should know about this

this (aka "the context") is a special keyword inside each function and its value only depends on how the function was called, not how/when/where it was defined. It is not affected by lexical scopes like other variables (except for arrow functions, see below). Here are some examples:

function foo() {
    console.log(this);
}

// normal function call
foo(); // `this` will refer to `window`

// as object method
var obj = {bar: foo};
obj.bar(); // `this` will refer to `obj`

// as constructor function
new foo(); // `this` will refer to an object that inherits from `foo.prototype`

To learn more about this, have a look at the MDN documentation.

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How to refer to the correct this

Use arrow functions

ECMAScript 6 introduced arrow functions, which can be thought of as lambda functions. They don't have their own this binding. Instead, this is looked up in scope just like a normal variable. That means you don't have to call .bind. That's not the only special behavior they have, please refer to the MDN documentation for more information.

function MyConstructor(data, transport) {
    this.data = data;
    transport.on('data', () => alert(this.data));
}

Don't use this

You actually don't want to access this in particular, but the object it refers to. That's why an easy solution is to simply create a new variable that also refers to that object. The variable can have any name, but common ones are self and that.

function MyConstructor(data, transport) {
    this.data = data;
    var self = this;
    transport.on('data', function() {
        alert(self.data);
    });
}

Since self is a normal variable, it obeys lexical scope rules and is accessible inside the callback. This also has the advantage that you can access the this value of the callback itself.

Explicitly set this of the callback - part 1

It might look like you have no control over the value of this because its value is set automatically, but that is actually not the case.

Every function has the method .bind ^[docs], which returns a new function with this bound to a value. The function has exactly the same behavior as the one you called .bind on, only that this was set by you. No matter how or when that function is called, this will always refer to the passed value.

function MyConstructor(data, transport) {
    this.data = data;
    var boundFunction = (function() { // parenthesis are not necessary
        alert(this.data);             // but might improve readability
    }).bind(this); // <- here we are calling `.bind()` 
    transport.on('data', boundFunction);
}

In this case, we are binding the callback's this to the value of MyConstructor's this.

Note: When a binding context for jQuery, use jQuery.proxy ^[docs] instead. The reason to do this is so that you don't need to store the reference to the function when unbinding an event callback. jQuery handles that internally.

Set this of the callback - part 2

Some functions/methods which accept callbacks also accept a value to which the callback's this should refer to. This is basically the same as binding it yourself, but the function/method does it for you. Array#map ^[docs] is such a method. Its signature is:

array.map(callback[, thisArg])

The first argument is the callback and the second argument is the value this should refer to. Here is a contrived example:

var arr = [1, 2, 3];
var obj = {multiplier: 42};

var new_arr = arr.map(function(v) {
    return v * this.multiplier;
}, obj); // <- here we are passing `obj` as second argument

Note: Whether or not you can pass a value for this is usually mentioned in the documentation of that function/method. For example, jQuery's $.ajax method ^[docs] describes an option called context:

This object will be made the context of all Ajax-related callbacks.

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Common problem: Using object methods as callbacks/event handlers

Another common manifestation of this problem is when an object method is used as callback/event handler. Functions are first-class citizens in JavaScript and the term "method" is just a colloquial term for a function that is a value of an object property. But that function doesn't have a specific link to its "containing" object.

Consider the following example:

function Foo() {
    this.data = 42,
    document.body.onclick = this.method;
}

Foo.prototype.method = function() {
    console.log(this.data);
};

The function this.method is assigned as click event handler, but if the document.body is clicked, the value logged will be undefined, because inside the event handler, this refers to the document.body, not the instance of Foo.
As already mentioned at the beginning, what this refers to depends on how the function is called, not how it is defined.
If the code was like the following, it might be more obvious that the function doesn't have an implicit reference to the object:

function method() {
    console.log(this.data);
}


function Foo() {
    this.data = 42,
    document.body.onclick = this.method;
}

Foo.prototype.method = method;

The solution is the same as mentioned above: If available, use .bind to explicitly bind this to a specific value

document.body.onclick = this.method.bind(this);

or explicitly call the function as a "method" of the object, by using an anonymous function as callback / event handler and assign the object (this) to another variable:

var self = this;
document.body.onclick = function() {
    self.method();
};

or use an arrow function:

document.body.onclick = () => this.method();

Here are several ways to access the parent context inside a child context -

1. You can use the bind() function.
2. Store a reference to context/this inside another variable (see the below example).
3. Use ES6 Arrow functions.
4. Alter the code, function design, and architecture - for this you should have command over design patterns in JavaScript.

1. Use the bind() function

function MyConstructor(data, transport) {
    this.data = data;
    transport.on('data', ( function () {
        alert(this.data);
    }).bind(this) );
}
// Mock transport object
var transport = {
    on: function(event, callback) {
        setTimeout(callback, 1000);
    }
};
// called as
var obj = new MyConstructor('foo', transport);

If you are using Underscore.js - http://underscorejs.org/#bind

transport.on('data', _.bind(function () {
    alert(this.data);
}, this));

2. Store a reference to context/this inside another variable

function MyConstructor(data, transport) {
  var self = this;
  this.data = data;
  transport.on('data', function() {
    alert(self.data);
  });
}

3. Arrow function

function MyConstructor(data, transport) {
  this.data = data;
  transport.on('data', () => {
    alert(this.data);
  });
}