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Since its discovery, the muon has provided information which has
been central to our understanding of the standard model
of subatomic physics. From its lifetime we get the Fermi
weak-coupling constant G_{?mu}. With its decay we studied the V-A weak
interaction, and have learned about lepton flavor conservation.
From negative muon capture on the nucleus we learned
about the weak couplings induced by the strong interaction. From its
anomalous magnetic moment we learned that the muon is a point particle,
but with a mass scale which provides a relative sensitivity of 40,000 to
higher-mass scales, compared to the electron's anomaly. We have learned
about hadronic and weak radiative corrections, along with a
significant sensitivity to potential new, as yet undiscovered,
virtual particles. In this talk I will give an overview of this
physics, with a special focus on the muon g-2 experiment at Brookhaven,
and lepton dipole moments in general.
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