Graphene has attracted much attention in recent years due to its extraordinary electronic, optical, magnetic, thermal, and mechanical properties. Despite continuing theoretical and experimental success, the unique physical properties of graphene remain underused and underappreciated. The key challenge in harnessing of the unique properties of graphene is the difficulty of reliable manipulation of well-dispersed graphene. Chemical and physical functionalization of graphene has become a focus of especial interest, because they can not only stabilize, but also induce new properties of graphene. This review summarizes the intriguing physical properties of chemically oxidized and noncovalently modified graphene, and graphene-based nanocomposites with polymer matrices or nanoparticles. Along with introducing the physical properties of functionalized graphene, their potential applications in diverse research areas are discussed.