Crossover networks are introduced as a new type of interconnection network for applications in optical computing, optical switching, and signal processing. Crossover networks belong to the class of multistage interconnection network. Two variations are presented, the half-crossover network and the full crossover network. An optical system which implements both networks is proposed and demonstrated. Crossover networks can be implemented using the full space-bandwidth product of the optical system with minimal loss of light. It is shown that crossover networks are isomorphic to other multistage networks such as the Banyan and perfect shuffle.