The muon g-2 in the standard model: a review of the calculation of hadronic contributions

In this talk I will review the status of the standard model calculation of the muon g-2. After a brief discussion of the QED and EW contributions I will concentrate on the hadronic ones, which are responsible for most of the final theoretical uncertainties. I will start with the hadronic vacuum polarization (HVP) first as calculated with a dispersive, data-driven approach, and then on the lattice, concentrating in particular on the result by the BMW collaboration. I will then discuss the hadronic light-by-light (HLbL) contribution, which has recently also become amenable to a dispersive, data-driven approach. Also this contribution can be calculated on the lattice and recently two collaborations have presented their results, which I will also briefly discuss. I will conclude with an outlook on possible future improvements in the calculation of these hadronic contributions.