  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 moment of the 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. These experiments, along
with searches for the lepton flavor violating decays $\mu \to e \gamma$ and
$\mu^- + A \to e^- + A$, provide a path to the high-energy frontier through
precision measurements.
