Organic integrated circuits are undergoing rapid development with the extensive research on organic semiconducting materials and the performance improvement of organic field-effect transistors. Organic integrated circuits not only cover all the major circuit types, their complexity, degree of integration, and performance have also been improved in recent years. In this review, recent advances in the design and fabrication of integrated circuits based on organic field-effect transistors are reported. The circuits are categorized into digital and analog, which are discussed in detail centering on the structure, fabrication process, and performance. In addition, progress in the modeling and simulation of organic integrated circuits are discussed as well, as they are key issues for the future development of organic electronics.