The advent of implantable biomaterials has revolutionized medical treatment, allowing the development of the fields of tissue engineering and medical bionic devices (e.g., cochlea implants to restore hearing, vagus nerve stimulators to control Parkinson's disease, and cardiac pace makers). Similarly, future materials developments are likely to continue to drive development in treatment of disease and disability, or even enhancing human potential. The material requirements for implantable devices are stringent. In all cases they must be nontoxic and provide appropriate mechanical integrity for the application at hand. In the case of scaffolds for tissue regeneration, biodegradability in an appropriate time frame may be required, and for medical bionics electronic conductivity is essential. The emergence of graphene and graphene-family composites has resulted in materials and structures highly relevant to the expansion of the biomaterials inventory available for implantable medical devices. The rich chemistries available are able to ensure properties uncovered in the nanodomain are conveyed into the world of macroscopic devices. Here, the inherent properties of graphene, along with how graphene or structures containing it interface with living cells and the effect of electrical stimulation on nerves and cells, are reviewed.