Leading-edge regenerative medicine can take advantage of improved knowledge of key roles played, both in stem cell fate determination and in cell growth/differentiation, by mechano-transduction and other physicochemical stimuli from the tissue environment. This prompted advanced nanomaterials research to provide tissue engineers with next-generation scaffolds consisting of smart nanocomposites and/or hydrogels with nanofillers, where balanced combinations of specific matrices and nanomaterials can mediate and finely tune such stimuli and cues. In this review, we focus on graphene-based nanomaterials as, in addition to modulating nanotopography, elastic modulus and viscoelastic features of the scaffold, they can also regulate its conductivity. This feature is crucial to the determination and differentiation of some cell lineages and is of special interest to neural regenerative medicine. Hereafter we depict relevant properties of such nanofillers, illustrate how problems related to their eventual cytotoxicity are solved via enhanced synthesis, purification and derivatization protocols, and finally provide examples of successful applications in regenerative medicine on a number of tissues.