  Searches for the permanent electric dipole moments (EDMs) of molecules,
atoms, nucleons and nuclei provide powerful probes of CP violation both within
and beyond the Standard Model (BSM). The interpretation of experimental EDM
limits requires careful delineation of physics at a wide range of distance
scales, from the long-range atomic and molecular scales to the short-distance
dynamics of physics at or beyond the Fermi scale. In this review, we provide a
framework for disentangling contributions from physics at these disparate
scales, building out from the set of dimension four and six effective operators
that embody CP violation at the Fermi scale. We survey existing computations of
hadronic and nuclear matrix elements associated with Fermi-scale CP violation
in systems of experimental interest, and quantify the present level of
theoretical uncertainty in these calculations. Using representative BSM
scenarios of current interest, we illustrate how the interplay of physics at
various scales generates EDMs at a potentially observable level.
