  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.
