CPLS

CPLS (short for Corner Permutation and Last Slot) is an algorithm set used to solve the last F2L slot (usually FR) and permute the last layer corners while preserving EO. CPLS leaves the solver with a 2gen last layer, which may be solved in one look using 2GLL (84 algs) or in two using OCLL and EPLL which contants only 11 algs and can be solved using R U moves.
Although seemingly hard to recognize, CPLS can be very beneficial, especially for onehanded solvers if fast 2generator algorithms are used.
Contents
History
CPLS was proposed by Baian Liu in 2009. The name initially only referred to the CPLC subset which solves the F2L corner + CP.
However, CPLS here refers to solving the last F2L pair + CP because the LS suffix in cubing often indicates the last pair being solved (compare ZBLS,OLS, VLS, WVLS etc.) and thus prevents confusion for people unfamiliar with CPLS. If one wants to clearly distinguish between the "original CPLS" and the "new CPLS", they can be referred to as CPLC and Full CPLS, respectively.
Subsets
Full CPLS is grouped into subsets depending on the F2L case they solve and then by their corner permutation.
Naming by CP case
Below, only the subsets for the individual F2L cases are listed. The naming for the different CPs of each F2L case is obtained by adding the following F2L letters to the subset, depending on the CP of the U layer corners.
SSolved CP 
DDiagonal swap 
RAdjacent swap on R 
BAdjacent swap on B 
LAdjacent swap on L 
FAdjacent swap on F 
Naming by F2L case
CPLC
CPLC, the "original CPLS", stands for Corner Permutation and Last Corner and solves the last LL corner and CP. It consists of 26 algorithms and is grouped into the following six subsets depending on the F2L corner, which is the same classification that is used for CLS:
C 
I 
Im 
 
+ 
O 
CPLE
CPLE stands for Corner Permutation Last Edge and solves the last F2L edge and CP. It only covers F2L case 25 and consists of only 6 algorithms.
Recognition
The different CPLS cases can be recognized by putting the F2L corner into one position and then comparing the stickers of the corners which can be seen. This system uses the relationships same, opposite and adjacent, which is similar to standard CxLL recognition. A more indepth guide for this recognition can be found here.
Example Solves
The following ZZd solve by raven shows the method in action:
Scramble: F' U R2 U' R2 U' B2 D2 B2 U R2 F2 L2 B L' D R2 B2 L2 U x2 B' F' R F D R' B2 U' L2 U2 L2 U' L // XXEOCross U' L U L' // F2L1 U' D R' U2 R U' R' U' R D' // CPLS U R' U' R U R U2 R' U' R' U R U' R U' R' U2 // 2GLL