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• Graphene oxide (GO) has potential applications in biomedical fields. • The functionalization of graphene include two general routes i.e. covalent and non-covalent functionalization. • GO with different surface functionalization has been used as nano- carriers for loading of chemotherapy drugs. • GO-based smart drug delivery systems responsive to environmental stimulations have also been studied. The field of nanoscience has blossomed over the last two decades and the importance of nanotechnology has increased in areas such as computing, sensors, biomedicine, and many other applications. In the present study, recent important advances in the functionalization of graphene with an emphasis on the physical properties upon tailored modification have been reviewed. It has been observed that functionalization cannot only stabilize graphene's unique properties but also introduce some new properties. The functionalization of graphene can be done with different methods like covalent functionalization, non-covalent functionalization, and with the decoration of nanoparticles. In this study, we put forward functionalization of graphene by polymers with different methods such as by direct linking of polymeric chains to the graphene surface or by the controlled growth of the polymeric chains at graphene surface or by decorating with polymers. The exceptional in-plane properties of graphene that are more complete exfoliation of graphite towards single graphene sheets with excellent mechanical, thermal, electrical, and barrier properties. The biological applications for the treatment of deadly diseases like cancer by functionalized nano-graphene oxide (NGO) have reviewed in depth. The application of NGO for drug delivery for gene therapy treatment has also been discussed in this review. [ABSTRACT FROM AUTHOR]