Electroweak baryogenesis may solve one of the most fundamental questions we
can ask about the universe, that of the origin of matter. It has become clear
in the past few years that it also poses a multi-faceted challenge. In order to
compute the tiny primordial baryonic excess, we probably must invoke physics
beyond the standard model (an exciting prospect for most people), we must push
perturbation theory to its ``limits'' (or beyond), and we must deal with
nonequilibrium aspects of the phase transition. In this talk, I focus mainly on
the latter issue, that of nonequilibrium aspects of first order transitions. In
particular, I discuss the elusive question of ``weakness''. What does it mean
to have a weak first order transition, and how can we distinguish between weak
and strong? I argue that weak and strong transitions have very different
dynamics; while strong transitions proceed by the usual bubble nucleation
mechanism, weak transitions are characterized by a mixing of phases as the
system reaches the critical temperature from above. I show that it is possible
to clearly distinguish between the two, and discuss consequences for studies of
first order transitions in general. (Invited talk given at the ``Electroweak
Physics and the Early Universe'' workshop, Sintra, March 23-25, 1994.)Comment: 16 pages, 4 figures not included (can be obtained from
hep-ph/9403310, or by request) RevTeX, DART-HEP-94/0