Graphene is the first carbon-based two dimensional atomic crystal and has gained much attention since its discovery by Geim and co-workers in 2004. Graphene possesses a large number of material parameters such as superior mechanical stiffness, strength and elasticity, very high electrical and thermal conductivity, among many others. It is the strongest and the most stretchable known material, which has the record thermal conductivity and very high intrinsic mobility, as well as being completely impermeable. Numerous favorable properties of graphene make it a potential promising material for applications in biomedicine. A large surface area, chemical purity and the possibility for its easy functionalization allow graphene to provide opportunities for drug delivery. Its unique mechanical properties suggest applications in tissue engineering and regenerative medicine. However, like other nanomaterials, graphene may pose a bio-hazard. In this article, we present a systematic review on the synthesis of graphene, various approaches for the fabrication of nanocomposites of graphene and their applications in biomedicine. A very detailed review is presented on how graphene and its nanocomposites are currently exploited for drug delivery, cancer therapy, gene delivery, biosensing and regenerative medicine. Finally, the safety and toxicity associated with graphene are also discussed.