Just Use Petrus

Just Use Petrus, or JUP for short, was created by Will Schmidt. It was designed with cubes like the 6x6 and 7x7 in mind, and is not suited for 4x4.
The Steps
1. Build two opposite centers
2. Solve a "Petrus Block" and remaining center pieces as bars (see display image above). Use methods similar to OBLBL or Yau5 to accompl
3. Solve five more edges with edge orientation, using the unsolved centers to allow more flexibility when solving edges.
4. Finish the centers while pairing the remaining edge wings, forming a Petrus block, and finish the last two edges
5. Solve F2L, then use COLL and EPLL for last layer. PLL parity should be included for EPLL when solving even layered puzzles
Pros
 Start 3x3 stage with edge orientation and a 2x2x3 Petrus block formed.
 Designed with 6x6 and 7x7 in mind
 Also prevents OLL parity on even layered puzzles
Cons
 Solving the Petrus block is a less efficient way to solve centers
 Edge pairing sometimes will often lead FD and parts of BL/BR to have edge pieces, leading to extra lookahead
Just use Petrus variations
There are several other substeps that can be used WV and ZBLL which completes the entire last layer in a single algorithm.