  From the famous experiments of Stern and Gerlach to the present, measurements
of magnetic dipole moments, and searches for electric dipole moments of
``elementary'' particles have played a major role in our understanding of
sub-atomic physics. In this talk I discuss the progress on measurements and
theory of the magnetic dipole moments of the electron and muon. I also discuss
a new proposal to search for a permanent electric dipole moment (EDM) of the
muon and put it into the more general context of other EDM searches.
