TCLL
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TCLL or Twisty Corners of Last Layer is an advanced 2x2 method proposed in 2013 by Robert Yau and Chris Olson based off a study into RoFL (ROtten First Layer) by Stefan Pochmann. It is efficient and is very good for those who can 1look their 2x2 solves and cancel into algorithms. It can be divided into 3 subsets: regular CLL, TCLL (where the misoriented corner in DR faces to the right) and TCLL+ (where the corner faces to the front). There are 43 algorithms for each TCLL set and 40 for the CLL.
Steps
 Solve a layer (one corner can be twisted in place)
 TCLL
Pros
 Can easily be 1looked in almost all cases fairly easily.
 Lots of cancellations can be formed between the layer and the algorithm
 Building a layer with a twisted corner is much shorter than building a full layer
 Can have ridiculously easy solves
Cons
 It is not generally recommended to use TCLL as a stand alone method
 Beginners may find it difficult to 1look solves and take advantage of the cancellations
 Approximately 2 Times more algorithms than CLL, EG1 or EG2
Example Solves
 R' F' R2 F R' U' F2 R' U'
 x2 y' (Canceling moves instead of doing U2 R U2 R) U2 F R F' R U
 F' R U' R' U F2 R' U2 R2
 y' L' U' L' F' L F U2 L' U2 L
 U R' F R' U2 R F' R U'
 z2 U' (Canceling moves instead of doing R U' R') R U2 R' U2 R U2 R' U
 R' F U R F2 R U' R2 U
 x L2 U2 R U R' U' R U2 R' F' R U R' F'
 U2 F2 U' F U' F' R' F' U2
 x' y' U F2 R U2 R' U R' F R F' R U' R'
 U R2 F' U R U2 R F2 U2
 x' U2 R y U' F R' F' R2 U R'
 U2 F' R' U' F2 U' R2 U R2
 x2 U F' R F' R U R2 U' R U R'