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. © 2004 American Institute of Physics