I did them for about two months in 2011. They are one of the best things a weight-training individual can do. They train mental focus, and rep execution (you want to make sure each rep is the same, to get through them). They are very difficult - mostly the mental strength required to face them & get them done. It can build to a serious dread of the gym & almost a fear. Done well, they take about three minutes. Do a quick set of pullovers - and you're done.
Your presses do not have to follow squats - Rippetoe recommends this, but Bill Starr and Brooks Kubik have written about doing them first. You can almost always get your squats after you press, but not always the other way around. I do my presses (bench, overhead) and arm work prior to squats. It works, and will work well if followed consistently.
I know you asked it of Oldster - I hope he doesn't mind if I chime in too. They are best for someone who knows how to squat well enough to do 20 consecutive decent reps. A novice is still building the habit of going to the gym thrice weekly, learning basic techniques, and can still make increases with 5x3 or 5x5 programs. I did them after about a year of training, starting with 185x20 (1RM of 355lb). I would increase the weight when I could get 25 total reps. I got up to 245x20.
An excellent article regarding the 20 rep breathing squat:
http://ditillo2.blogspot.com/2008/06...-400-x-20.html