The Dirac equation is the relativistic version of the Schrödinger equation, and hence unsurprisingly it plays a central role in relativistic (where the speed of light is finite) quantum mechanics. It is known that for certain nonlinear models, as the speed of light tends to infinity, the Dirac equation converges on finite time scales to the Schrödinger equation. Here I will explain how recent uniform (in the speed of light) estimates for small data solutions to the cubic Dirac equation can be used to prove that the non relativistic limit in fact holds on global time scales in dimensions $d>1$. In particular we have convergence of scattering states and wave operators from the Dirac equation to the corresponding Schrödinger equation. This is joint work with Sebastian Herr.