Scaffolds are important to tissue regeneration and engineering because they can sustain the continuous release of various cell types and provide a location where new bone-forming cells can attach and propagate. Scaffolds produced from diverse processes have been studied and analyzed in recent decades. They are structurally efficient for improving cell affinity and synthetic and mechanical strength. Carbon nanotubes are spongy nanoparticles with high strength and thermal inertness, and they have been used as filler particles in the manufacturing industry to increase the performance of scaffold particles. The regeneration of tissue and organs requires a significant level of spatial and temporal control over physiological processes, as well as experiments in actual environments. This has led to an upsurge in the use of nanoparticle-based tissue scaffolds with numerous cell types for contrast imaging and managing scaffold characteristics. In this review, we emphasize the usage of carbon nanotubes (CNTs) and CNT–polymer composites in tissue engineering and regenerative medicine and also summarize challenges and prospects for their potential applications in different areas.