The origins of CP violation are not understood, although the magnitude of the baryon asymmetry of the Universe tells us that there are mechanisms at work beyond the Standard Model. Most “new physics” predicts the existence of fundamental-particle electric dipole moments (EDMs) that are orders of magnitude larger than the SM prediction, and so EDM measurements provide severe constraints upon physics beyond the SM such as supersymmetry. In this talk I will discuss the latest measurement of the neutron EDM, as well as progress towards the next-generation experiment which promises to be two orders of magnitude more sensitive still.