CFCE

CFCE (Cross, F2L, CLL, and ELL), is an LBL method, similar to CFOP, where you make a cross and then the first two layers are solved simultaneously by filling in the 4 F2L (First 2 Layers) slots with pairs. Then, you solve the last layer in two steps. Instead of solving it by doing OLL then PLL, you solve it by first doing CLL (Corners of the last layer) and then, doing ELL (Edges of the Last Layer).
Contents
The Steps
1. Cross
First, make a cross on any side of the cube. This entails solving all of the edges with a given color to their proper positions.
2. F2L
In this step you fill in the slots where the corners of the cross are missing. For each insertion, a corner and an edge are placed simultaneously. There are 41 basic cases for this step, but it can be learned intuitively.
3. CLL
Next, solve all last layer corners using 1 of 42 algorithms. Alternatively, you can do 2look CLL, which only requires 39 algorithms.
4. ELL
Finally, you solve all the last layer edges using 1 of 29 algorithms. Alternatively, you can do 2look ELL, which only requires 27 algorithms.
History
Guus Razoux Schultz used the full method in the 1982 world championship finals, where he got second place. In the early 2000s Masayuki Akimoto adopted the method and set the first Asian 3x3 single record of 17.79s at the 2003 world championship.
Since then, CFCE adoption has been hampered by the dubious belief that lastlayer recognition is harder for CFCE than for CFOP, and that the ELL algorithms are bad. However recent years have seen renewed interest in the method.
 Why does no one use CFCE to solve the Rubik's Cube?, r/Cubers (Reddit), 2018
See also
F2L 
CLL 
U cases  T cases  L cases  S cases  S cases  H cases  pi cases  edit 
ELL 
Pure flips  EPLLs  3cycles  In position but flipped  No edges in position  edit 