Yau

The Yau method is a faster method than the beginner method, used by the world record holders.
The first step of Yau is to solve two opposite center pieces.

Bottom center solved
Bottom center solved
Top center solved
Top center solved

Next, solve 3 edges of the bottom center(The center you are going to solve the cross on)

Bottom center solved
Bottom center solved
3 edges solved
3 edges solved

Next, solve the 3 centers for the 3 edges.

3 Center pieces solved
3 Center pieces solved
3 Center pieces solved
3 Center pieces solved

Next, solve the remaining edge and center piece.

3 Center pieces solved
3 Center pieces solved
Completed center and edge pieces
Completed center and edge pieces

Next, solve the remaining edge and center piece. Then, solve the cube like a 3x3.

Completed center and edge pieces
Completed center and edge pieces
Completed 4x4
Completed 4x4

Just like in beginner's Method, there is a weird thing about 4x4, and that is parity errors. These is due
to the absence of center pieces in the 4x4. There are two parity cases
and there are algorithms to solve each of them.

First Parity case
First Parity case
Second Parity case
Second Parity case

Now you have a completed 4x4!

Below is an in-depth tutorial on the 4x4 Yau Method

To see world records, click here!
For online tutorials, click here!

This method can be applied to bigger cubes such as 5x5. See video below