A number of recent advances in the Physics of the Muon (g - 2) experiments are described outlining the expectations of future improvements of the statistical and systematic errors of the technique. A comparison between the spin and beam dynamics of the two muon (g - 2) experiments under preparation at FNAL and at J-PARC shows that they are both well under control. It may be possible to use magnetic focusing for the FNAL experiment, especially if a decision is made to run with negative muons. Finally, a polarized proton beam could be used to measure the B-field in case of magnetic focusing