Multicomponent, synergistic and multifunctional nanostructures have taken over the spotlight in the realm of biomedical nanotechnologies. The most prospective materials for bone regeneration today are almost exclusively composites comprising two or more components that compensate for the shortcomings of each one of them alone. This is quite natural in view of the fact that all hard tissues in the human body, except perhaps the tooth enamel, are composite nanostructures. This review article highlights some of the most prospective breakthroughs made in this research direction, with the hard tissues in main focus being those comprising bone, tooth cementum, dentin and enamel. The major obstacles to creating collagen/apatite composites modeled after the structure of bone are mentioned, including the immunogenicity of xenogeneic collagen and continuously failing attempts to replicate the biomineralization process in vitro. Composites comprising a polymeric component and calcium phosphate are discussed in light of their ability to emulate the soft/hard composite structure of bone. Hard tissue engineering composites created using hard material components other than calcium phosphates, including silica, metals and several types of nanotubes, are also discoursed on, alongside additional components deliverable using these materials, such as cells, growth factors, peptides, antibiotics, antiresorptive and anabolic agents, pharmacokinetic conjugates and various cell-specific targeting moieties. It is concluded that a variety of hard tissue structures in the body necessitates a similar variety of biomaterials for their regeneration. The ongoing development of nanocomposites for bone restoration will result in smart, theranostic materials, capable of acting therapeutically in direct feedback with the outcome of in situ disease monitoring at the cellular and subcellular scales. Progress in this research direction is expected to take us to the next generation of biomaterials, designed with the purpose of fulfilling Daedalus’ dream - not restoring the tissues, but rather augmenting them.