The anomalous magnetic moment of the muon a_mu has long served as a probe of new physics at low energies. After decades of improvements to its theoretical determination based on the Standard Model (SM) as well as to its direct experimental measurement, a_mu is now known at the level of 0.37 ppm [Theory Initiative White Paper 2020] and 0.19 ppm [dominated by the Fermilab Muon g-2 experiment], respectively. However, the direct measurement and the theoretical prediction are discrepant at the level of 5.1 standard deviations. The total uncertainty of the SM prediction is dominated by effects of the strong interaction, notably the contributions from hadronic vacuum polarisation (HVP) and from hadronic light-by-light scattering. I describe recent progress in the determination of both quantities. In particular, a strong tension has emerged between lattice QCD base calculations of the HVP and the dispersive determination that underlies the White Paper 2020. Resolving it has the potential of bringing the SM prediction for a_mu into agreement with its experimental value.