Advanced and expert
XCross, predicting the first pair, ZBLL, and what is still to come (CLS, BLE). Fewer moves, fewer pauses, and skipping steps of the last layer.
XCross
An XCross solves the cross together with the first F2L pair, so the first pair is done by the time the cross is. It needs more planning than a plain cross, because you are placing five pieces in inspection instead of four.
Build up to it: first make a cross plus a pair you can see is easy, and look for cases where the first pair is placed almost for free while the cross pieces go in. Keep it only when it saves moves overall.
Predicting the first pair
While you execute the cross, keep track of where your first pair's corner and edge end up. When the cross finishes you already know what to do next, which removes the pause between the cross and F2L.
Practise by solving only the cross and then saying out loud what your first pair is before moving. The review page shows if the pause after the cross has shrunk.
ZBLL: the last layer in one algorithm
ZBLL solves the whole last layer in one go when the last-layer edges are already oriented, whatever the corners are. That covers 493 cases up to U turns before and after the algorithm: 21 are the PLLs you already know and 472 are new.
For a random last layer, the edges are oriented about 1 time in 8, so ZBLL is a tool you reach for when it comes up, and you need a plan (such as an edge-orienting F2L pair) to make it come up more often. It is the usual way to go from 2-look to a one-look last layer.
The trainer groups the 472 cases by what the corners look like (Sune, Antisune, H, Pi, L, T, U). Learn one group at a time. The algorithms in the trainer are the shortest I found using R, U and F turns, and every one is checked by computer, but the community often prefers other algorithms for fingertricks. Replace any you do not like.
Still to come
CLS (orient the last-layer corners while inserting the last corner) and BLE (orient the last-layer corners while inserting the last edge, given the last-layer edges are already oriented and the last corner is placed) will follow once their case sets are generated and checked the same way as the others.