The muon magnetic moment and physics beyond the standard model

We review the role of the anomalous magnetic moment of the muon a_μas a powerful probe of physics beyond the Standard Model (BSM), taking advantage of the final result of the Fermilab g-2 experiment and the recently updated Standard Model value. This review provides both a comprehensive summary of the current status, as well as an accessible entry point for phenomenologists with interests in dark matter, Higgs and electroweak or neutrino and flavour physics in the context of a wide range of BSM scenarios. It begins with a qualitative overview of the field and a collection of key properties and typical results. It then focuses on model-independent, generic formulas and classifies types of BSM scenarios with or without chiral enhancements. A strong emphasis of the review are the connections to a large number of other observables -- ranging from the muon mass and the muon--Higgs coupling and related dipole observables to dark matter, neutrino masses and high-energy collider observables. Finally, we survey a number of well-motivated BSM scenarios such as dark photons, axion-like particles, the two-Higgs doublet model, supersymmetric models and models with leptoquarks, vector-like leptons or neutrino mass models. We discuss the impact of the updated Standard Model value for a_μand of complementary constraints, exploring the phenomenology and identifying excluded and viable parameter regions.