Lattice QCD+QED and the muon anomalous magnetic moment

Experimental efforts aim at reducing the uncertainty on the measurement of the muon anomalous magnetic moment by a factor of four in the coming years. Huge efforts are therefore under way to improve the theory prediction for this quantity where the dominant uncertainty is due to hadronic effects, in particular the hadronic vacuum polarisation. This talk reviews the remarkable theoretical and numerical progress made by the lattice QCD community in reliably predicting these effects.