The early universe matter is composed of quarks, gluons and leptons. Then the quarks and gluons form hadrons. Further nuclei appear. The evolution can be classified as the phase transition from the chiral symmetric to the chiral symmetry broken and that from deconfinement to confinement. Because phase transitions are governed by nonperturbative interaction(s) and the nonperturbative QCD is extremely complicated, only recently some progresses have been made. We discuss here briefly the phase transitions in the Dyson-Schwinger equation approach of QCD.