This review deals with the theory of four-fermion interactions in curved spacetime. Starting with the D-dimensional Minkowski spacetime (2 ≤ D ≤ 4) the effective potential in the leading order of 1/N-expansion is calculated and the phase structure of the theory is investigated. Using the same technique the effective potential for composite operator ψ̄ψ in four-fermion models is calculated under the following circumstances:
