  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.
