Abstract
In the standard electroweak theory, if the Higgs boson mass is comparable with the weak scale, the electroweak transition is weakly first order, and proceeds via bubble nucleation. It is shown that the Universe supercools beyond the point where phase equilibrium is possible. When true-vacuum bubbles nucleate, they expand at velocities of the order of the speed of light until they fill the Universe. These considerations are important for the recently proposed electroweak baryogenesis mechanisms.