  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.
