### Abstract

The phases of QCD and QCD like theories in the chemical potential temperature plane are reviewed. Although the situation along the temperature axis has been explored extensively by means of first principle calculations, the status of lattice QCD simulations at nonzero chemical potential is yet far from settled. The reason is the phase of the fermion determinant which invalidates probabilistic methods to evaluate the partition function. Both the average of this phase factor and the order parameter for the chiral phase transition are related to the spectral flow of the Dirac eigenvalues. A criterion for the severity of the sign problem is formulated. Explicit analytical results are obtained in the microscopic domain of QCD where observables can be evaluated by means of random matrix methods.