Owing to their unique mechanical, electrical, optical, and thermal properties, carbon nanostructures including carbon nanotubes and graphenes show great promise for advancing the fields of biology and medicine. Many reports have demonstrated the promise of these carbon nanostructures and their hybrid structures (composites with polymers, ceramics, and metal nanoparticles, etc.) for a variety of biomedical areas ranging from biosensing, drug delivery, and diagnostics, to cancer treatment, tissue engineering, and bioterrorism prevention. However, the issue of the safety and toxicity of these carbon nanostructures, which is vital to their use as diagnostic and therapeutic tools in biomedical fields, has not been completely resolved. This paper aims to provide a summary of the features of carbon nanotube and graphene-based materials and current research progress in biomedical applications. We also highlight the current opinions within the scientific community on the toxicity and safety of these carbon structures.