QCD at non-zero temperature and density from the Lattice

The study of systems as diverse as the cores of neutron stars and heavy-ion collision experiments requires the understanding of the phase structure of QCD at non-zero temperature, T, and chemical potential, μq. We review some of the difficulties of performing lattice simulations of QCD with μq≠0, and outline the re-weighting method used to overcome this problem. This method is used to determine the critical endpoint of QCD in the (μq,T) plane. We study the pressure and quark number susceptibility at small μq.