  The dynamics of phase transitions plays a crucial r\^ole in the so-called
interface between high energy particle physics and cosmology. Many of the
interesting results generated during the last fifteen years or so rely on
simplified assumptions concerning the complex mechanisms typical of
nonequilibrium field theories. In particular, whenever first order phase
transitions are invoked, the metastable background is assumed to be
sufficiently smooth to justify the use of homogeneous nucleation theory in the
computation of nucleation rates of critical bubbles. In this talk I present the
results of numerical simulations which were designed to quantify
``smoothness''; that is, how the contribution from nonperturbative subcritical
fluctuations may spoil the homogeneity assumption of nucleation theory. I then
show how the numerical results can be understood {\it quantitatively} in terms
of a simple analytical model of subcritical thermal fluctuations. Encouraged by
the success of the model in matching the numerical results, I apply it to the
standard model electroweak phase transition.
