The following materials based on four allotrope types of nanocarbons were investigated: (1) fullerene C60 and hybrid C60/Ti films, (2) composites of synthetic polymers and carbon nanotubules (i.e., carbon nanohorns and carbon nanotubes), (3) graphene-based materials (films and three-dimensional scaffolds), and (4) nanocrystalline diamond-based materials (films and nanofibrous scaffolds loaded with nanodiamond particles). In general, all these substrates provided a good support for colonization with human osteoblast-like cells of the lines MG-63, Saos-2 and U-2 OS, primary osteoblasts, and also human mesenchymal stem cells (hMSC). In the case of fullerenes C60, this was true for aged, i.e., 1-year-old, films. Fresh films, i.e., 1-week-old, had a decreased number of initially adhering cells, with less spreading, growth, metabolic activity and viability, though no DNA damage was detected. In the case of C60/Ti composite films, both fresh and aged films supported cell colonization well. The improved cell performance was attributed to structural changes in fullerene molecules, such as fragmentation, oxidation and polymerization, which occur during aging or co-deposition of C60 and Ti. The addition of single-wall carbon nanohorns or multi-wall carbon nanotubes to a terpolymer of polytetrafluoroethylene, polyvinyldifluoride and polypropylene (PTFE/PVDF/PP) markedly improved the adhesion and growth of bone cells, while no significant changes in cell behavior were found on polysulfone after it had been enriched with the carbon nanotubules mentioned here. Graphene-based films and scaffolds stimulated the adhesion and osteogenic differentiation of bone-forming cells even in the absence of cell adhesion-mediating molecules and differentiation factors in the cell culture medium. Nanocrystalline diamond films proved to be excellent substrates for cell adhesion, growth and osteogenic differentiation, and this cell behavior was further improved by boron doping (concentration of 133–6700 ppm) or by oxygen termination of these films. The addition of diamond nanoparticles to nanofibrous poly(lactide-co-glycolide) (PLGA) scaffolds increased the proliferation of hMSC and supported the adhesion and growth of MG-63 cells in an extent similar to cell culture polystyrene. However, on nanofibrous poly(L-lactide) scaffolds with diamond nanoparticles, the growth of MG-63 cells decreased with increasing nanoparticle concentration.