In summary, we achieved the goals originally planned in our proposal and conducted several additional studies which broadened up the output of our work and contributed to a more general understanding of the origin of hardness enhancement in superhard nanocomposites and heterostructures. The focus of the first part of our work has been the combined ab initio DFT calculation and thermodynamic modelling in order to study the possibility of spinodal decomposition and formation of nanocomposites with high thermal stability. Besides of the Ti-Si-N and Ti-B-N systems which have been published, we studied also several other nitride and oxide systems. These results are summarized in the Ph. D. Thesis of S.H. Sheng and in preparation for publications. Using ab initio DFT we conducted in depth studies of the mechanical properties and of the mechanism of tensile de-cohesion and shear deformation for heterostructures consisting of few nm thick TiN slabs with one monolayer of interfacial SiN. It has been shown that, although the bulk fcc-SiN is unstable, the I ML SiN layer is strongly heteroepitaxially stabilized. The weakest links are the Ti-N bonds adjacent to that interface where the de-cohesion and shear occur. The heterostructures (and nanocomposites) with I ML SiN are stronger than those with 2 ML because of increasing weakening of the Ti-N bonds in the latter case. Moreover, we have clarified why ReB2 cannot be superhard, and that the recently reported high hardness of c-BCs is not an intrinsic property but a result of its nanosize nature. These results are very important in the general discussion of how to design strong materials.