  Electric dipole moments are extremely sensitive probes of physics beyond the
Standard Model. A vibrant experimental program is in place, with the goal of
improving existing bounds on the electron and neutron electric dipole moments
by one or two orders of magnitude, while testing new ideas for the measurement
of electric dipole moments of light ions, such as the proton and the deuteron,
at a comparable level. The success of this program, and its implications for
physics beyond the Standard Model, relies on the precise calculation of the
electric dipole moments in terms of the couplings of CP-violating operators
induced by beyond-the-Standard-Model physics. In light of the nonperturbative
nature of both QCD at low energy and of the nuclear interactions, these
calculations have proven difficult, and are affected by large theoretical
uncertainties. In this talk I will review the progress that has been achieved
on different aspects of the calculation of hadronic and nuclear EDMs, the
challenges that remain to be faced, and the implications for our understanding
of physics beyond the Standard Model.
