Two synthesis routes to graphene/polycaprolactone composites are introduced and the properties of the resulting composites compared. In the first method, mixtures are produced using solution processing of polycaprolactone and well dispersed, chemically reduced graphene oxide and in the second, an esterification reaction covalently links polycaprolactone chains to free carboxyl groups on the graphene sheets. This is achieved through the use of a stable anhydrous dimethylformamide dispersion of graphene that has been highly chemically reduced resulting in mostly peripheral ester linkages. The resulting covalently linked composites exhibit far better homogeneity and as a result, both Young's modulus and tensile strength more than double and electrical conductivities increase by 14 orders of magnitude over the pristine polymer at less than 10 per cent graphene content. In vitro cytotoxicity testing of the materials showed good biocompatibility resulting in promising materials for use as conducting substrates for the electrically stimulated growth of cells.