Phase Transitions in Dense and Hot Matter

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.