Most studies of the QCD phase diagram tacitly assume that the different phases are homogeneous in space. However, there are good arguments that inhomogeneous phases could also be present. In this talk I focus on inhomogeneous chiral-symmetry breaking phases, where the quark condensate varies in space. Model calculations suggest that the first-order chiral phase transition, including the critical endpoint, could be removed from the phase diagram when inhomogeneous phases are included. More recently similar results have also been obtained from Dyson-Schwinger studies of QCD.
