The thermal dilepton rate at NLO at small and large invariant mass

We report on a recent next-to-leading order perturbative determination of the dilepton rate from a hot QCD plasma for frequency and momentum of the order of the temperature and for much smaller invariant mass $Msim gT$. We briefly review the calculation, which generalizes the previous one for the photon case ($M=0$). We then analyze the consequences of the new calculation for the extraction of the photon rate from the small mass dilepton measurements. We then review a recent NLO determination at large $M$ and we show how to match and merge its results with the low-mass ones, resulting in a single rate which is NLO-accurate over the phenomenologically relevant region.