Graphene based nanomaterials are being used experimentally to deliver therapeutic agents to cells or tissues both in vitro and in vivo. However, substantial challenges remain before moving to safe and effective use in humans. In particular, it is recognised that graphene molecules undergo complex interactions with solutes, proteins or cellular systems within the body, and that these interactions impact significantly on the behaviour or toxicity of the molecule. Approaches to overcome these problems include modification of the graphene or its combination with other molecules to accentuate favourable characteristics or modify adverse interactions. This has led to an emerging role for graphene as one part of highly-tailored multifunctional delivery vehicles. This review examines the knowledge that underpins present approaches to exploit graphene in therapeutics delivery, discussing both favourable and unfavourable aspects of graphene behaviour in biological systems and how these may be modified; then considers the present place of the molecule and the challenges for its further development.