Abstract: New schemes of structural classification for carbon phases and nanostructures have been proposed, which are based on the types of chemical bonds formed and the numbers of the nearest neighbors with which each atom forms covalent bonds. The classification schemes can describe not only the known phases, but also new phases and nanostructures. New phases can be derived by linking, superpositioning or cutting precursor structures. The classification scheme has been used to predict diamond polymorphs, yielding thirty diamond-like phases that consist of atoms in equivalent crystallographic positions and eighteen of which were predicted for the first time.