We examine the muon's electric dipole moment \dmu from a variety of theoretical perspectives. We point out that the reported deviation in the muon's g-2 can be due partially or even entirely to a new physics contribution to the muon's {\em electric} dipole moment. In fact, the recent g-2 measurement provides the most stringent bound on \dmu to date. This ambiguity could be definitively resolved by the dedicated search for \dmu recently proposed. We then consider both model-independent and supersymmetric frameworks. Under the assumptions of scalar degeneracy, proportionality, and flavor conservation, the theoretical expectations for \dmu in supersymmetry fall just below the proposed sensitivity. However, non-degeneracy can give an order of magnitude enhancement, and lepton flavor violation can lead to \dmu of order 10−22 e cm, two orders of magnitude above the sensitivity of the \dmu experiment. We present compact expressions for leptonic dipole moments and lepton flavor violating amplitudes. We also derive new limits on the amount of flavor violation allowed and demonstrate that approximations previously used to obtain such limits are highly inaccurate in much of parameter space
