In recent years, researchers prepared composite conductive inks with high conductivity, high thermal conductivity, strong stability, and excellent comprehensive mechanical properties by combining carbon-based materials such as graphene and carbon nanotubes with metal-based materials. Through new electronic printing technologies, conductive inks can be used not only to promote the development of integrated circuits but also in various new electronic products. The conductive mechanism and the main types of conductive inks are introduced in this review. The advantages of electronic printing technology for preparing integrated circuits are analyzed. The research progress of fabricating integrated circuits with different electronic printing processes, such as screen printing, gravure printing, flexographic printing, and inkjet printing, are summarized. The development trend of carbon-based composite conductive ink for integrated circuits is prospected.