PBL
Permutation of both layers, abbreviated as PBL, is a step used in a number of 2x2x2 methods (and thus corners first methods). Specifically, the Ortega method and the Guimond method, perhaps the two most popular advanced 2x2x2 methods, both finish with a PBL step. When solving only corners, PBL has five unsolved cases, which can be recognized by the number of adjacent color pairs on each side that are correctly permuted (a solved side has 4 pairs, an adjacent corner swap has 1 pair, and a diagonal corner swap has 0 pairs), so the unsolved cases (denoted by counting number of color pairs on top and bottom) are 0+0, 1+0, 1+1, 4+0, and 4+1. Algorithms for PBL (for 2x2x2 or CF) can be found at the CxLL pages (the grey cases in the topmost line).
It is actually possible, in theory, to do PBL in one step for 3x3x3 or Square1  in this case we would be permuting not only corners but the whole layers. No speedcubing method actually uses this, though, because there are about 800 cases in total and recognition is very difficult. For the Square1, many methods do PBL in two steps, by first solving the corners of both layers and then doing the edges of both layers. Even though two layers are being permuted at once, though, solvers conventionally refer to the steps as simply CP and EP.
Algorithms
Swap UF Corners (1+4)

Swap ULayer Diagonal (0+4)

Swap UF + DF Corners (1+1)

Swap U + D Diagonal (0+0)

Swap UB Corners + DLayer Diagonal (1+0)

Swap UB + DB Corners (1+1)

The first two algorithms (Y perm and A perm) only affect the top layer, and because of that, they can be used in LBL methods.
Note that D moves are the same as U + y, just a different notation, what you do for real is something in between. The effect of it is that you transform F moves to R or L (D R makes the same turns as U F + y').
See also
External links