Muon g-2: hadronic contributions and isospin breaking corrections from the lattice

Anomalous magnetic moment of the muon, a_mu=(g-2)_mu/2, is one of the most precisely measured quantities in particle physics and it provides a stringent test of the standard model. With the planned improvement of the experimental precision at Fermilab and at J-PARC further reduction of the theoretical uncertainty is required, in order to be able to resolve the current discrepancy between the experimental measurement of a_mu and its theoretical prediction, and potentially gain insight into new physics. The dominant source of the uncertainty in the theoretical prediction of a_mu are the errors of the hadronic contributions. In this talk I will explain several promising approaches for a precise determination of the leading hadronic contribution to a_mu. Finally, I will discuss the relevance of a precise estimate of the size of the isospin breaking effects for obtaining this quantity from lattice QCD simulations with sub-percent precision.