QCD calculations of thermal photon and dilepton production

In this talk, I review new developments of QCD calculations of photon and dilepton production rates in a Quark-Gluon plasma. All the rates are now known up to $O(\alpha_s)$ both for photons and dileptons, thanks to the resummation of multiple scatterings. For dileptons, a direct numerical calculation on the lattice attempted recently will also be discussed.