Electric dipole moments as probes of new physics

We review several aspects of flavour-diagonal CP violation, focussing on the role played by the electric dipole moments (EDMs) of leptons, nucleons, atoms and molecules, which consitute the source of several stringent constraints on new CP-violating physics. We dwell specifically on the calculational aspects of applying the hadronic EDM constraints, reviewing in detail the application of QCD sum-rules to the calculation of nucleon EDMs and CP-odd pion-nucleon couplings. We also consider the current status of EDMs in the Standard Model, and on the ensuing constraints on the underlying sources of CP-violation in physics beyond the Standard Model, focussing on weak-scale supersymmetry.