Graphene has attracted great interest for its superior physical, chemical, mechanical, and electrical properties that enable a wide range of applications from electronics to nanoelectromechanical systems. Functionalization is among the significant vectors that drive graphene towards technological applications. While the physical properties of graphene have been at the center of attention, we still lack the knowledge framework for targeted graphene functionalization. In this critical review, we describe some of the important chemical and physical processes for graphene functionalization. We also identify six major challenges in graphene research and give perspectives and practical strategies for both fundamental studies and applications of graphene (315 references).