Multifunctional fiber-reinforced polymer (FRP) composites provide an ideal platform for next-generation smart composites applications including structural health monitoring, electrical and thermal conductivity, energy storage and harvesting, and electromagnetic interference shielding without compromising their mechanical properties. Recent progress in carbon-based nanomaterials such as graphene and carbon nanotubes (CNTs) has enabled the development of many novel multifunctional composites with excellent mechanical, electrical, and thermal properties. However, the effective incorporation of such carbon nanomaterials into FRP composites using scalable, high-speed, and cost-effective manufacturing without compromising their performance is challenging. This review summarizes the recent progress on graphene and CNT-based FRP composites, their manufacturing techniques, and their applications in smart composites. Current technical challenges and future perspectives on smart FRP composites research to facilitate an essential step toward moving from research and development-based smart composites to industrial-scale mass production are also discussed.