Graphene and its derivatives have been widely employed in the manufacturing of novel composite nanomaterials which find applications across the fields of physics, chemistry, engineering and medicine. There are many techniques and strategies employed for the production, functionalization, and assembly of graphene with other organic and inorganic components. These are characterized by advantages and disadvantages related to the nature of the specific components involved. Among many, biomolecules and biopolymers have been extensively studied and employed during the last decade as building blocks, leading to the realization of graphene-based biomaterials owning unique properties and functionalities. In particular, biomolecules like nucleic acids, proteins and enzymes, as well as viruses, are of particular interest due to their natural ability to self-assemble via non-covalent interactions forming extremely complex and dynamic functional structures. The capability of proteins and nucleic acids to bind specific targets with very high selectivity or the ability of enzymes to catalyse specific reactions, make these biomolecules the perfect candidates to be combined with graphenes, and in particular graphene oxide, to create novel 3D nanostructured functional biomaterials. Furthermore, besides the ease of interaction between graphene oxide and biomolecules, the latter can be produced in bulk, favouring the scalability of the resulting nanostructured composite materials. Moreover, due to the presence of biological components, graphene oxide-based biomaterials are more environmentally friendly and can be manufactured more sustainably compared to other graphene-based materials assembled with synthetic and inorganic components. This review aims to provide an overview of the state of the art of 3D graphene-based materials assembled using graphene oxide and biomolecules, for the fabrication of novel functional and scalable materials and devices.