New Physics searches with muons: Theoretical review

We summarize current issues related to New Physics searches with muons with focuses on the ratio of magnetic moments of the muon and the proton, needed for the muon gμ-2 determination; on using the bound-electron g-2 to help independently check the persisting discrepancy between the measured gμ-2 and the Standard Model; and on the bound-muon decay as a background for the muon-electron conversion.