The minimal model programme is an attempt to classify algebraic varieties up to birational equivalence. In dimensions at least three, minimal models are not unique, and are linked by special birational maps called flops. I’ll say some things about the above, before turning to noncommutative methods and discussing a certain invariant of threefold flops, the Donovan—Wemyss contraction algebra. Time permitting, I’ll also say some things about a derived version of the contraction algebra, and indicate why it classifies (possibly singular) threefold flops. The talk will be loosely based on some of the contents of https://arxiv.org/abs/1911.09626.