A generalization of the BCS theory of superconductivity that describes the crossover of a system between a BCS state and Bose–Einstein condensation (BEC). The concept of BCS–BEC crossover has been applied to high-temperature superconductivity and ultracold atoms. In the latter case it is possible to study the BCS–BEC crossover in a controlled way using Feshbach resonances. It is hoped that this might give some insights into the mechanism of high-temperature superconductivity.