Lattice QCD simulations have entered the precision era. Thanks to the combined efforts of several lattice collaborations, the masses, leptonic and semileptonic decay rates of light pseudoscalar mesons are presently known, in QCD, with sub-percent relative errors. At this level of precision radiative QED and SU(2)-breaking corrections cannot be neglected and have to be taken into account with the required non-perturbative accuracy. This can in principle be done by performing lattice simulations of QCD+QED.
In this talk, we discuss the framework for including isospin-breaking corrections in leptonic and semileptonic weak decays of hadrons using lattice simulations. For these quantities the presence of infrared divergences in intermediate stages of the calculation makes the procedure much more complicated than is the case for the hadronic spectrum.
We present first numerical results for the π_μ2(γ) and K_μ2(γ) decay rates and for the form factors contributing to the amplitudes for the radiative decays P → lνlγ, where P is a pion, kaon, D or D_s meson and l is a charged lepton. Finally, a critical discussion of future developments will be given.