A fundamental problem in modular representation theory is whether, having bounded a natural invariant known as the defect of a block, there are only a finite number of blocks of finite groups up to Morita equivalence. Donovan’s conjecture is that the answer is “yes”, and its resolution would profoundly influence the way we view the subject. I will give the background necessary to state the conjecture and attempt to give some insight into it, before describing some recent work using the Classification of Finite Simple Groups.