High Precision Calculations of the Higgs Boson Mass

In this paper we are going to review the status of the computations of the perturbative quantum corrections to the Higgs boson mass in the Standard Model and in its supersymmetric extensions. In particular, supersymmetric theories require a very accurate computation of the Higgs boson mass, which includes corrections up to even three-loop level, since their predictions are limited by theoretical uncertainties. A discussion about these uncertainties in the context of the minimal and next to minimal supersymmetric standard models is included.