QCD pressure up to four loops at finite temperature and density

In recent years the perturbative expansion of the pressure of massless QCD has been driven to order g^6ln(g) at high temperatures and finite chemical potentials, which has required calculations up to three-loop order in the full theory and up to four-loop order in three-dimensional effective theories. In the present paper we briefly review the theoretical background behind this work and explain some of the methods used in the computations.