There are many procedures available, so here is a look at the eight most common types of cosmetic plastic surgery. Breast Augmentation Breast augmentation refers to procedures that increase the size or change the shape of the breasts. Breast Augmentation This is likely the most well-known form of cosmetic surgery since it is one of the most talked-about when women get it done. Plus, there are many different variations of it. The main two include breast lifts and enlargements.