Let's look at OLL & PLL parity

Parity is a speedsolvers nightmare, but what actually is it and why does it occur?

Parity only occurs on 4x4 cubes and up. You cannot get parity on a 2x2 or 3x3 cube due to the nature of the puzzle itself. A 4x4 however, is different, as you have floating centers (apposed to fixed centers). Parity can occur if you put the wrong center piece in the wrong slot. It's hard to describle but on every face on a 4x4 you have 4 center pieces that each have a specific slot they must go in. If you put a center piece in . the wrong slot you have a chance of getting parity during your solve.

OLL Parity

On the 4x4 there is only one OLL case which is shown above.
This is when 2 pieces of the last layer are orientated incorrectly. 

PLL Parity

There are a few PLL parity cases on the 4x4. These are when the last layer is orientated correctly but they are in the incorrect position to solve using the regular 3x3 method.

OLL Parity on the 4x4

OLL ALGORITHM 1

r2 B2 U2 l U2 r' U2 r U2 F2 r F2 l' B2 r2

PLL Parity on the 4x4

PLL ALGORITHM 1

(Uu)2 (Ll)2 U2 l2 U2 (Ll)2 (Uu)2 

PLL ALGORITHM 2

L2 D (Ff)2 (Ll)2 F2 l2 F2 (Ll)2 (Ff)2 D' L2 

PLL ALGORITHM 3

(Uu)2 (Ll)2 U2 l2 U2 (Ll)2 (Uu)2 F' U' F U F R' F2 U F U F' U' F R 

PLL ALGORITHM 4

(Uu)2 (Ll)2 U2 l2 U2 (Ll)2 (Uu)2 R U' L U2 R' U R L' U' L U2 R' U L' U