Probing new CP-odd physics with electric dipole moments

We discuss the utility of precision probes for flavour-diagonal CP violation, namely searches for electric dipole moments (EDMs) of nucleons, atoms and molecules, in accessing new CP-odd physics at high energy scales. We summarise the effective field theory analysis of the observable EDMs in terms of a general set of CP-odd operators at 1 GeV, and the ensuing model-independent constraints on new physics. We also discuss the ensuing constraints on SUSY models, focussing in particular on the sensitivity to new CP-odd thresholds associated with dimension-five operators beyond the minimal supersymmetric standard model (MSSM), and comment briefly on constraints on minimal models of electroweak baryogenesis.