Mechanical properties, such as elasticity modulus, tensile strength, elongation, hardness, density, creep, toughness, brittleness, durability, stiffness, creep rupture, corrosion and wear, a low coefficient of thermal expansion, and fatigue limit, are some of the most important features of a biomaterial in tissue engineering applications. Furthermore, the scaffolds used in tissue engineering must exhibit mechanical and biological behaviour close to the target tissue. Thus, a variety of materials has been studied for enhancing the mechanical performance of composites. Carbon-based nanostructures, such as graphene oxide (GO), reduced graphene oxide (rGO), carbon nanotubes (CNTs), fibrous carbon nanostructures, and nanodiamonds (NDs), have shown great potential for this purpose. This is owing to their biocompatibility, high chemical and physical stability, ease of functionalization, and numerous surface functional groups with the capability to form covalent bonds and electrostatic interactions with other components in the composite, thus significantly enhancing their mechanical properties. Considering the outstanding capabilities of carbon nanostructures in enhancing the mechanical properties of biocomposites and increasing their applicability in tissue engineering and the lack of comprehensive studies on their biosafety and role in increasing the mechanical behaviour of scaffolds, a comprehensive review on carbon nanostructures is provided in this study.