Lattice results for many hadronic parameters relevant for flavor physics and precision tests of the Standard Model have reached the level of accuracy that isospin breaking corrections need to be included. We discuss some of the subtleties related to the implementation of QED on the lattice and the computation of correlation functions of charged hadrons. We give particular emphasis to the realization of massive-QED on the lattice and present preliminary results for the electromagnetic corrections to the hadronic vacuum polarization of the photon, which is relevant for theoretical estimates of the muon anomalous magnetic moment.