The following is an excerpt from the new book, 5/3/1 Forever. This book outlines how to program all areas of your training including assistance work. Yes, that's right; no more questions about assistance work. Everything is tied up, nice and tight AND allows for a lot of personal choices. Each and every program detailed in the book has a specific assistance profile which allows you to plug in a variety of different movements; all customized to you.
There is certainly a plethora of choices for assistance work but one of the most popular is using bodyweight movements. Here is the introduction to that section:
"I am a huge fan of using bodyweight movements for assistance work. On their own, bodyweight assistance work is limiting. Bodyweight-only proponents like to sell you that anyone can get big and strong using push-ups and their brethren. They often cite Hershel Walker and Olympic gymnasts as their examples – but Walker played pro-football and won the Heisman. Olympic gymnasts are in the Olympics. So let’s not use the exception to prove the rule. However, bodyweight work as assistance—when used as part of a balanced program of barbell training, jumping, throwing, mobility work and conditioning—becomes another animal.
One reason why I like bodyweight assistance work is that it allows a lifter to get more volume in his training without much harm to his joints. One can recover much faster from bodyweight work than barbell training. Of course, this becomes an issue if the lifter uses crappy form; just watch someone doing half-rep pushups or using excessive momentum during a chin-up/pull-up. It is a joke. If you want to get something out of an exercise, do it right. So do your push-ups and dips with a full range of motion, pausing at the top and bottom for a second. Don’t flail around like an idiot when you hang from a bar – you aren’t impressing anyone with your self-destructive lifting.
Bodyweight assistance work can also act as a marker for strength and (for the lack of a better term) fitness levels. For example, expecting someone to perform 10 chin-ups/pull-ups, 25 push-ups, 15 dips and 10 hanging leg raises isn’t asking for much; how many times have you seen someone ask for a specialized squat plan or who can’t figure out why his deadlift is stuck yet can’t perform these very basic physical tasks? If a lifter doesn’t have the strength to lift his legs to a chin bar for 10 slow, consecutive reps he doesn’t have the basic abdominal strength to get him very far in the main lifts. If he can’t do 20 back raises, do you really think it’s his lack of front squats that are impeding his deadlift? So cover the basics before you even think about moving on to something more advanced."