Isospin symmetry is an almost exact property of strong interactions which is explicitly violated in the Standard Model by the small difference between the up and down quark masses and by their different electric charges. The effects of this breaking introduce corrections to physical quantities at the percent level. Although these contributions are small, they play a crucial role in the description of atomic matter. Given the highly non perturbative behaviour of strong nteractions at the hadronic scale, isospin breaking corrections can be computed from first principles through QCD+QED ab initio numerical simulations on the lattice. Nowadays, with the increasing precision of the experimental determinations of many physical quantities, and in some cases with the improvement of the theoretical predictions, the control over isospin breaking effects is becoming phenomenologically relevant. In this talk, I present a method to evaluate on the lattice the leading isospin breaking effects due to both quark masses and QED interactions. Results are obtained for several quantities, including a determination of the up and down quark masses and the charged/neutral pseudoscalar meson mass splittings. Moreover, a new strategy has been recently proposed for the first time to compute electromagnetic effects in hadronic processes using lattice simulations. The method can be applied, for example, to the leptonic and semileptonic decays of light or heavy pseudoscalar mesons. For these quantities the presence of infrared divergences in intermediate stages of the calculation makes the procedure more complicated than in the case of the hadronic spectrum, for which some lattice calculations already exist. In this talk, I illustrate the method for the leptonic decays of pseudoscalar mesons. Its practical implementation, although challenging, is within reach of the present lattice technology. In this respect, results for the leading order electromagnetic and strong isospin breaking corrections to pion and kaon decay rates are evaluated for the first time.