As very large integrated circuits reach a critical dimension of a few tens of nanometers, conventional silicon based technology is facing a big challenge. tNew materials and architectures are becoming a hot topic, and much effort is being put into developing molecular electronic devices as a part of nanoelectronics. The current primary architectures of molecular electronic devices are field effect transistors and crossbar switches, and crossbar structures are attracting world-wide attention due to theireasy integration. The principles and processing of molecular electronic devices based on crossbar architecture are; the implementation of logic circuits based on crossbars, and recent progress in this area are described. The prospects and problems of crossbar circuits are also summarized.