Status of Lattice Studies of the QCD Phase Diagram

Determining the QCD phase diagram is a pressing task in view of its relevance for nuclear and astro-particle physics programmes. We review the current status of lattice calculations of the phase diagram in the (T,\mu_B)-plane for baryon chemical potentials \mu_B < 500 MeV. At \mu_B=0, simulations of staggered fermion actions predict the quark hadron transition to be a crossover in the continuum limit. As a baryon chemical potential is turned on, there is mounting evidence on coarse lattices for the crossover to weaken, rather than turning into a true phase transition at a critical point, as predicted by earlier simulations.