  In this conference proceeding, I discuss in detail the deconfinement to quark
matter that takes place at large densities and/or temperatures. The first-order
phase transition that is assumed to appear beyond a critical point gives rise
to mixtures of phases when more than one globally conserved quantity (such as
charge fraction) is imposed. The modifications caused by these mixtures of
phases in the QCD phase diagram can have consequences on signals of the
existence of quark matter expected to be created in heavy-ion collisions, as
well as supernova explosions and neutron-star mergers.
