The phase diagram of dense quark matter in compact stars

The phase structure of strongly interacting matter at high densities with the possible existence color superconducting phases of deconfined quark matter is one of the challenging problems for modern quantum field theories of hot and dense matter. The conditions for deconfinement of quarks under high compression and excitation of hadronic matter may be fulfilled in the relatively cold but dense centers of neutron stars as well as in relativistic heavy-ion collisions. In the pesent lecture we review results obtained within an approach based on chiral quark models of the Nambu-Jona-Lasinio (NJL) type. We discuss the effect of neutrality constraints which are of relevance for compact stars and the selfconsistent determination of the strange quark mass for the QCD phase diagram. An outlook to signals of the deconfinement phase transition and of possible color superconductivity states of matter from the evolutionary behavior of compact objects is given.