There has been increasing interest in the use of pristine graphene in biomedical applications, but its use is limited by its hydrophobicity and lack of functional groups by which to tether molecules, meaning that biological applications of pristine graphene rely on non-specific adsorption of molecules. Furthermore, pristine graphene cannot be used in-vivo due to its poor aqueous dispersibility. Functional groups are introduced to graphene to overcome these problems, but many functionalisation methods cause significant disruption to the extended Ï-system of graphene, from which its favourable properties arise. The aim of this thesis was to address the limitations of using pristine graphene outlined above. The solution proposed was the edge-specific sulfonation and thiol functionalisation of pristine graphene, based upon electrophilic aromatic substitution. The nature of these reactions means that they should cause minimal defect formation, occurring selectively at existing defects and edges of the graphene sheet. The sulfonation of graphene was selected to increase the aqueous dispersibility of pristine graphene, while the thiol functionalisation would provide a means by which to tether molecules covalently to the graphene sheet. The functionalisations were confirmed using a range of analyses, which indicated a low level of new defect formation, as well as demonstrating both the presence of the target functional groups and the change in aqueous dispersibility of the graphene sheets. Furthermore, the functionalisation was shown to be edge-specific by attaching a fluorescent protein to thiol functional groups on the edges. G-SO3 was incorporated into a polymer layer-by-layer (LbL) construct, for use in wound healing applications, together with analogous constructs containing graphene oxide (GO) and sulfonate-functionalised GO (GO-SO3). The constructs were characterised, to assess the effect of different functionalisations on the coverage of graphene. Analysis confirmed the presence of G-SO3, GO and GO-SO3 in the constructs, but indicated a lower graphene coverage for the G-SO3 construct, thought to be a result of the lower number of functional groups in this material. The biocompatibility of G-SO3, GO and GO-SO3 LbL constructs was tested on 3T3 Swiss Albino fibroblast cells and human mesenchymal stem cells. In addition, the differentiation of stem cells on these graphene-containing surfaces was monitored and compared to published work on graphene-family nanomaterials. The biocompatibility studies revealed that cell adhesion and proliferation were dictated by extracellular matrix (ECM) protein adsorption on the LbL constructs. The substrates able to bind higher amounts of ECM protein were found to show greater cell adhesion and proliferation, with ECM protein binding correlated to the roughness and surface chemistry of the constructs. Future applications would be to introduce alternative functional groups to graphene, using the principles outlined in this thesis. In addition, there is potential for the attachment of a variety of biologically relevant molecules to functionalised graphene sheets. This could lead to the use of pristine graphene in many biomedical applications.