Precision measurements of the muon anomalous magnetic moment from the decade-old BNL experiment have revealed an intriguing excess relative to the theoretical calculations of the same quantity. I review the status of this 3-sigma discrepancy, and zoom onto the New Physics explanations that it has generated. The discrepancy may be a hint of new massive particles near the electroweak scale, a possibility that comes under the increasing pressure from the LHC results, which so far show no signs of new physics. An alternative possibility, which has been in focus of my research for some time, is the correction to the muon anomaly from a light, MeV-to-GeV range, very weakly coupled New Physics sector. I review the status of this explanation in light of new experimental searches of the so-called "dark photon", discussing a few remaining viable options and new proposals for their future experimental tests.