The muon anomalous magnetic moment, g-2, is one of the most sensitive low-energy tests of the Standard Model and is sensitive to a variety of hypothetical new physics models. g-2 of the muon is also one of the few observables with a tantalizing deviation between the SM theory prediction and the measurement. In the talk, I will first review the SM theory prediction, with emphasis on new developments in the QCD and electroweak contributions. Then I will discuss several cases of new physics. In some cases, the new physics contributions to g-2 can be very large, even with heavy new particles. In other cases, the new physics contributions are small, no matter what the new particle masses and couplings are. Finally, the precision of the theory predictions is discussed, and precision corrections in new physics models are explained.