Bodybuilding is an ever expanding activity. Anyone who goes to a gym or works out at home with weights is essentially bodybuilding. Recreational bodybuilders just want to be more muscular and improve their body composition. Most are looking for that abdominal six pack as part of their training.
Training regimens vary according to how serious you are about gaining muscle, losing body fat, and getting stronger. The aim for most bodybuilders is to maximize muscle mass and minimize body fat. As far as the training, more volume is needed than for those looking mainly to maximizing strength, especially in sports with weight classes.
We'll outline some of the more common training regimens followed by all levels of bodybuilders, as well as some that are more extreme, including high intensity training, high intensity interval training, the use of drop sets, one set to maximum, etc.
Reading the section on Power Sports will give you some more information as to why maximizing muscle mass should be disconnected to maximizing strength, since more volume of training, usually with higher reps and sets, or training to failure with a weight that's relatively light compared to those looking to maximize strength, are necessary to maximize muscle cell size.