Smart structures can help to resolve many issues related to conventional materials that are being used in different industries. Shape memory alloys (SMAs) are smart materials with better actuation response, vibration damping characteristics, and large strain recovery, making them good candidates due to their high strength and corrosion resistance for various engineering applications. The performance of fiber-reinforced polymer (FRP) composite materials that are replacing many conventional materials due to their good strength, stiffness, and lightweight potential especially in fuel-consuming industries such as aerospace and automotive, can further be improved by impregnation with SMAs. This review discusses the SMA-reinforced FRP composites, leading to shape memory hybrid composite materials, the issues and limitations in composite manufacturing, and their uses in different research arenas including impact and damping applications, seismic protection applications, crack closure applications, shape morphing applications, and self-deployable structures.