This is a video that explains pretty much everything you'll ever want to know (and possibly more) about commutators and conjugates. Please note: I did not necessarily use the "best" commutator/conjugate for every example in this video. I mostly just used the first commutator/conjugate that I saw. All Rubik's cube animations in this video are from: http://www.randelshofer.ch/rubik/virtualcubes/v