  The present knowledge of the QCD phase diagram based on simulations of
lattice QCD is summarised. The main questions are whether there is a critical
point in the QCD phase diagram and whether it is related to a chiral phase
transition. It is shown that QCD at imaginary chemical potentials has a rich
phase structure, which can be determined in a controlled way without sign
problem and which severely constrains the phase structure at real chemical
potentials.
