The muon is a heavy cousin of the electron and has a gyromagnetic ratio of 2 in the classical limit, which was predicted by Dirac. In QED it receives an anomalous magnetic moment which was computed by Julian Schwinger at leading order. Today, in QED it is evaluated to very high loop order, and also receives corrections from virtual processes in the vacuum as dictated by the laws of quantum field theory, which have to be evaluated in a variety of ways. It is also measured at high precision today at Fermilab, whose recent results confirm the value measured at Brookhaven about 20 years ago. More data is being gathered to lower the uncertainty. The theoretical value which is known at high precision deviates from the experimental measurement at several standard deviations. The quantity is also measured on the lattice with larger errors. In this talk we will review these developments and also speak about our own results that have played an important role in lowering the uncertainties in the theoretical hadronic vacuum polarization contributions.