**Abstract:** A flop is a birational transformation between threefolds which does not alter the canonical bundle; the elementary flops are those which are an isomorphism outside of a smooth curve of genus 0. Around 25 years ago, Miles Reid classified elementary flops when the normal bundle of the curve in the threefold is O(-1)+O(-1) or O+O(-2); around 15 years ago, Sheldon Katz and the speaker classified elementary flops in general. In modern times, one would like to wrap D-branes on such a curve and understand the resulting physics; however, the existing classification theorem is not precise enough to allow one to do this. We will describe a new way to look at flops, based on the McKay correspondence and motivated by the attempt to understand the physics of D-branes wrapping rational curves. (This talk is based on joint work with Carino Curto.)