  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, mu_q. We review some of the
difficulties of performing lattice simulations of QCD with non-zero mu_q, and
outline the re-weighting method used to overcome this problem. This method is
used to determine the critical endpoint of QCD in the (mu_q,T) plane. We study
the pressure and quark number susceptibility at small mu_q.
