  The electroweak phase transition provides the most attractive framework to
account for the baryon asymmetry of the universe. Comparing results of
perturbative and nonperturbative studies is not straightforward, however, due
to the different coupling constant definitions. The perturbative one stems from
the $\bar{\mathrm{MS}}$ subtraction scheme, while the nonperturbative one uses
the static quark potential. The momentum-space perturbative static potential is
calculated in the SU(2)--Higgs model, and is Fourier transformed into
coordinate space. Based on the connection between the coupling constants,
two-loop perturbative and 4-dimensional lattice simulation results are
contrasted. The thermodynamical parameters of the phase transition indicate
that perturbative results are reliable only for low Higgs masses, far from the
endpoint. The value of the endpoint can be refined to $72.1\pm1.4$ GeV. The
Higgs mass range for which dimensional reduction yields reliable results is
identified. As an extension of the standard model, the MSSM is also studied.
Some useful trends are indicated by a simple one-loop perturbative approach:
baryogenesis requirements are more easily met if the stop is lighter thanthe
top; colour-breaking phase transition may be possible, etc. In order to perform
4D nonperturbative studies the supercomputer PMS was built at E\"otv\"os
University. The results and the techniques of the simulations of the bosonic
sector of the MSSM performed on PMS are presented. A phase diagram is given,
the bubble wall is studied. The cosmologically relevant part of the parameter
space is analysed. The results show that baryogenesis is possible within the
MSSM if $m_h\leq 103\pm 4$ GeV.
