  Recent developments on the four dimensional (4d) lattice studies of the
finite temperature electroweak phase transition (EWPT) are summarized. The
phase diagram is given in the continuum limit. The finite temperature
SU(2)-Higgs phase transition is of first order for Higgs-boson masses m_H<66.5
+/- 1.4 GeV. Above this endpoint only a rapid cross-over can be seen. The full
4d result agrees completely with that of the dimensional reduction
approximation. The Higgs-boson endpoint mass in the Standard Model (SM) would
be 72.1 +/- 1.4 GeV. Taking into account the LEP Higgs-boson mass lower bound
excludes any EWPT in the SM. A one-loop calculation of the static potential in
the SU(2)-Higgs model enables a precise comparison between lattice simulations
and perturbative results. The most popular extension of the SM, the Minimal
Supersymmetric SM (MSSM) is also studied on 4d lattices.
