  Standard theories of electroweak interactions are based on the concept of a
gauge symmetry broken by the Higgs mechanism. If they are placed in an
environment with a sufficiently high temperature, the symmetry gets restored.
It turns out that the characteristics of the symmetry restoring phase
transition, such as its order, are important for cosmological applications,
such as baryon asymmetry generation. We first briefly review how, by a
combination of analytic and numerical methods, the properties of the phase
transition can be systematically resolved for any given type of a (weakly
interacting) Higgs sector. We then summarise the numerical results available
for the Standard Model, and present a generic model independent statement as to
how the Higgs sector should differ from the Standard Model for the properties
of the transition to be very different. As an explicit example, we discuss the
possibilities available for a strong transition in the experimentally allowed
parameter region of the Minimal Supersymmetric Standard Model.
