LSE

LSE, also called L6E, short for Last Six Edges, is a possible last step in 3x3 speedsolving that solves the Mslice centers and edges (UF, UB, DF, DB) together with UL and UR edges. It is the last step of the Roux Method and the Ortega Method.
Possible approaches
LSE can be solved in various ways; Gilles Roux himself, the inventer of the Roux Method, advocates a flexible/semiintuitive approach to LSE without a strict division into substeps. The optimal approach is likely a combination of the approaches below.
Layersbased approach
 1. centers, BD, and FD
 2. ELL
This layerbased approach seems out of place in any method ending with LSE.
Original Roux
 1. Orient centers and edges
 2. Permute UR and UL edges
 3. Permute the M slice
The following two approaches are commonly used in Corners first methods.
Corners First approach 1
 1. Solve UL or UR
 2. Insert UL/UR while orienting the M slice
 3. Permute the M slice
Corners First approach 2
 1. Solve both UL and UR
 2. Orient and permute the M slice
Reduction to L5E has been proposed as an experimental approach.
L5E
 1. Centers and BD
 2. L5E
Orientation+Permutation
 1. Orient all edges
 2. Permute all edges with L6EP
L6EP

L6EP or LSEP is a subset of LSE that permutes the last six edges finishing the solve. Like LSE, it can be solved 2gen with only M and U moves. It is used in Corners First methods and Roux. For the latter, however, EOLR + 4c is more widespread than EO + L6EP.
A variation of it called "WaterZZ L6EP", where instead of the DB edge, the FR edge is permuted, is used in the WaterZZ method.
Possible approaches
Layersbased approach
 Solve the two D layer edges
 Finish the solve with EPLL
While this is easiest for solvers coming from CFOP, it is not very efficient.
Roux L6EP
 Permute UR and UL edges (Roux 4b)
 Permute the M slice (Roux 4c)
This approach is the most common as it is fully intuitive, very known due to the popularity of Roux and also pretty efficient.
One look L6EP
 Permute all six edges using one algorithm
While this is definitely the best approach in terms of ergonomics and movecount, it is rarely used due to the high amount of cases. However, since most cases are semiintuitive, learning can be done in a similar fashion to EOLR or intuitive F2L.