Carbon nanomaterials (CNMs) have been proposed as promising nanofillers for polymer composites because of their high surface area, structural flexibility, good mechanical strength, and their unique thermal, optical, and electronic properties. However, the strong van der Waals interactions between individual nanoparticles have limited the manipulation of CNMs and restricted their use in many promising fields. The functionalization of CNMs has attracted great interest on synthesis of complex structures, and helped establish different facile, scalable, controllable and low-cost methods to graft well-defined polymers onto the surfaces of CNMs. This review highlights the advances made in recent years on the functionalization chemistry of carbon nanotubes and graphene with polymers by both the "grafting from" and "grafting to" techniques. (C) 2016 Wiley Periodicals, Inc.