Motivated by the success and exhaustive research on carbon nanotubes (CNTs) based drug delivery, graphene, a two-dimensional; honey-comb crystal lattice has emerged as the rising star in recent years. Graphene is a flat monolayer of carbon atoms that holds many promising properties such as unparalleled thermal conductivity, remarkable electronic properties, and most intriguingly higher planar surface and superlative mechanical strength, which are attractive in biotechnological applications. Delivery of anti-cancer drugs using graphene and its derivatives has sparked major interest in this emerging field. The anti-cancer therapies often pose a limitation of insolubility, administration problems and cell penetration ability. In addition, systemic toxicity caused by lack of selective targeting towards cancer cells and inefficient distribution limits its clinical applications. Graphene nanocomposite is a promising tool to address these drawbacks. This review will focus on various synthesis and functionalization of graphene and graphene oxide for providing better solubility and targeted drug delivery at cancer cells. A more advanced and 'smart' graphene hybrid nanostructures that have several functionalities such as stimulus-response mediated delivery, imaging at release sites as well as transfection into cancer cells are also presented. A brief description on the challenges and perspectives for future research in this field is also discussed.