  Four-fermion interaction models are considered to be prototype models for
dynamical symmetry breaking.The present review deals with recent developments
in the studies of dynamical symmetry breaking in the four-fermion interaction
models and their extension in curved spacetime. Starting with the Minkowski
spacetime in dimension $D$ ($2 \leq D \leq 4$) the effective potential in the
leading order of $1/N$-expansion is calculated and the phase structure of the
theory is investigated. In curved spacetime curvature-induced phase transitions
are discussed in the circumstances where fermion masses are dynamically
generated. Subsequently a possibility of curvature- and temperature-induced or
curvature- and topology-induced phase transitions is discussed. It is also
argued that the chiral symmetry broken by a weak magnetic field may be restored
due to the presence of gravitational field. Finally some applications of
four-fermion models in quantum gravity are briefly described.
