  We discuss finite-size effects on homogeneous nucleation in first-order phase
transitions. We study their implications for cosmological phase transitions and
to the hadronization of a quark-gluon plasma generated in high-energy heavy ion
collisions. Very general arguments allow us to show that the finite size of the
early universe has virtually no relevance in the process of nucleation and in
the growth of cosmological bubbles during the primordial quark-hadron and the
electroweak phase transitions. In the case of high-energy heavy ion collisions,
finite-size effects play an important role in the late-stage growth of hadronic
bubbles.
