The “curly arrow” of Robinson and Ingold is the primary tool for describing and rationalizing reaction mechanisms. Despite this approach’s ubiquity and stellar success, its physical basis has never been clarified and a direct connection to quantum chemistry has never been found. Here we report that the bond rearrangements expressed by curly arrows can be directly observed in ab initio computations, as transformations of intrinsic bond orbitals (IBOs) along the reaction coordinate. Our results clarify that curly arrows are rooted in physical reality—a notion which has been challenged before—and show how quantum chemistry can directly establish reaction mechanisms in intuitive terms and unprecedented detail. Curly arrows from ab initio calculations: Curly arrows in reaction mechanisms are shown to correspond to changes in intrinsic bond orbitals (IBOs) along reaction paths. With this quantum chemical basis, even complex reaction mechanisms can be derived and visualized in a simple, direct, and intuitive form.