  After some introductory remarks about the prospects of first order phase
transitions in the early universe, we discuss in some detail the electroweak
phase transition. In the standard model case a clear picture is arising
including perturbative and nonperturbative effects. Since in this case the
phase transition is not strongly first order as needed for baryogenesis, we
discuss supersymmetric variants of the standard model, the MSSM with a light
stop$_R$ and a NMSSM model where this can be achieved. We conclude with some
remarks about the technical procedure and about possible effects of a strongly
first order electroweak phase transition including baryogenesis.
