The discovery of the interesting intrinsic properties of graphene, a two-dimensional nanomaterial, has boosted further research and development for various types of applications from electronics to biomedicine. During the last decade, graphene and several graphene-derived materials, such as graphene oxide, carbon nanotubes, activated charcoal composite, fluorinated graphenes and three-dimensional graphene foams, have been extensively explored as components of biosensors or theranostics, or to remotely control cell-substrate interfaces, because of their remarkable electro-conductivity. To date, despite the intensive progress in human stem cell research, only a few attempts to use carbon nanotechnology in the stem cell field have been reported. Interestingly, most of the recent in vitro studies indicate that graphene-based nanomaterials (i.e. mainly graphene, graphene oxide and carbon nanotubes) promote stem cell adhesion, growth, expansion and differentiation. Although cell viability in vitro is not affected, their potential nanocytoxicity (i.e. nanocompatibility and consequences of uncontrolled nanobiodegradability) in a clinical setting using humans remains unknown. Therefore, rigorous internationally standardized clinical studies in humans that would aim to assess their nanotoxicology are requested. In this paper we report and discuss the recent and pertinent findings about graphene and derivatives as valuable nanomaterials for stem cell research (i.e. culture, maintenance and differentiation) and tissue engineering, as well as for regenerative, translational and personalized medicine (e.g. bone reconstruction, neural regeneration). Also, from scarce nanotoxicological data, we also highlight the importance of functionalizing graphene-based nanomaterials to minimize the cytotoxic effects, as well as other critical safety parameters that remain important to take into consideration when developing nanobionanomaterials.