The possibility, often explored in the literature, that field theories exhibit metastable vacuum states in the background of a hot expanding universe is examined. By studying the finite-temperature effective potential for self-interacting scalar fields and also for scalar fields interacting with fermion fields, the conditions for the existence of a metastable vacuum are derived. The effects of asymmetries on the effective potential as well as of couplings of the scalar field to other fields on the kinetics of the phase transition are examined. Possible applications to electroweak symmetry breaking, the quark-hadron phase transition, and the primordial formation of nontopological solitons are briefly discussed.