The CFCE method

Pros:

• Less algs than CFOP
• Slightly lower average turn count for each solve
• CLL is a 2x2 speedsolving method as well so you learn two methods in one
• If transitioning from CFOP you can keep most F2L strategies

Cons:

• Harder to learn recognition that may be slower(?)
• Not used by many people
• Possibly lower max TPS due to M slices in final step
• Doesn't have as catchy of a name as CFOP
• influencing edges with F2L does not really help as many of the CLL algs will mess with the LL edges

The steps:

1. The cross
2. F2L or First two layers
3. CLL or Corners of Last Layer
4. ELL or Edges of Last Layer

The cross:

This step should be fairly easy as it is the same as most beginner methods as well as CFOP.
All you have to do is solve all the edges of one side (usually the white).
This step can take anywhere from 0-8 turns with an average of ~6.

First two layers:

This step is done by inserting a corner then inserting the matching equator layer edge. F2L can be done using anywhere from 0-41 algorithms.
If you would like to learn more about F2L either look up intuitive F2L on youtube or go here for F2L algs.

CLL:

My CLL algs

CLL has 42 cases separated by the corner pattern into 8 groups. For more CLL algs, try the speedsolving.com wiki or just click here.

ELL:

My ELL algs

ELL has a total of 29 cases 4 of which are PLLs and the rest are PLLs with edge flips except for the 3 pure-flips.
For more ELL algs go to speedsolving.com (although theirs aren't very good)

Overview:

The CFCE method has 71-112 algorithms depending on the number of F2L cases memorized.
Its main pro is that it has fewer total algs than CFOP while maintaining a similar or lower average turn count.
Using the speed-optimized algorithms given on this webpage and optimal F2L, the Rubiks cube can be solved in an average of <57 turns STM.