  We study numerically the real-time history of the cosmological electroweak
phase transition, as it may take place in the Standard Model or in MSSM for m_H
< m_W according to recent lattice results. We follow the nucleated bubbles from
the initial stages of acceleration and rapid growth, through collisions with
compression waves resulting in slowing down and reheating to T_c, until the
final stages of slow growth and evaporation. We find that collisions with
compression waves may make the bubble walls oscillate in the radial direction,
and that reheating to T_c takes generically place.
