Biketrials pedal hopHooking the front wheel
An amazing technique, for very high or vertical stuff if you can't land directly your bash guard or pedals in place. Not for the faint hearted forks (some would snap during the most critical phase). First you should know how to bunny hop properly.

1° Start by launching a bunny hop, just high enough to bring the front wheel on top of the obstacle.
2° Slam the bunny hop into the obstacle, with the front wheel clear above the upper edge. 3° Front brakes full on, keep your whole body moving forwards. 4° As the shoulders move beyond the bars, start to push up on your arms.
4° After pushing up, let your forward movement inertia bring you further over the bars and unlock the front wheel. 5° Complete the linear motion by extending the arms and let the front wheel loose again to roll forwards. 6° Pull up the bike further by lifting the arms in front of you, for a nice finish on the rear wheel (fully extended).
This technique works best with long frame geometries (the longer the better, as it gives more "wrapping" from the bike to the edge). Andrei makes it look easy, but that's really a top notch move.
See the move in a video and from a front view

The front wheel hook technique on a mod.
1° Slam the bunny hop into that wall, with the front wheel clearing the edge. 2° As the shoulders move beyond the bars, start to push up on your arms. 3° Complete the linear motion by extending the arms and let the front wheel loose again to roll forward.
Again, Matt is a beast at this stuff.
See that move in a video

Stamina needed
If you practice on something that is not too high, the first part of the move is quite easy, like a lazy bunny hop that does not even bring your crank up to the edge. But then the second part is truly spectacular. You must carry-on with the initial momentum to bring your shoulders beyond the edge of the wall, over the bars, and then push up in one boost to bring your whole body moving up again (a bit like in a static hop except that the rear wheel is not touching any ground). Then in the next sequence, pull up the bike with you one extra step to land at least the bash guard onto the edge, or possibly the rear wheel (like when finishing off a bunny hop). I guess it is a good idea to practise hooking the front wheel on sloped walls, before attacking vertical stuff.
video
Practise on sloppy walls
Springy forks
When attacking vertical walls, the strain on the fork is enormous, and some forks will just snap after too many sessions, typically on duty, with a nice potential for nasty crashes. (but hey...it's a top move). At the beginning, it's quite common to fall back, as you'll end up so much on the rear of your bike, with no proper support for the rear wheel. The trick is to avoid a full rigid stop when slamming the wall (a natural reflex). Instead, progressively absorb the horizontal deceleration without pushing back from the wall (that would break your forward momentum). As long as you are in that deceleration phase, you can still expect a decent grip from your tires.

At a Pro level: pushing the move further
Experienced riders will hook their front wheel on about anything. The pressure in the bars is really high, as when you hang to the front wheel, it tends to turn and go flat on the side of the fork. Being able to maintain the hooked position and hop directly to back-wheel is the most difficult part.
video
Matt going mad at a car
video
Cesar on a smooth skip
video
Waynio hanging to his front wheel