The most recent data on experimentally undiscovered carbon allotropes, predicted by the Density Function Theory (DFT), are reviewed. Classic carbon allotropes, graphenes, carbon nanotubes, fullerenes and their hybrids are being studied using DFT and related methods, resulting a host of potentially existing forms based on 5-, 6-, 7-member cycles and their distinct combinations. Also known are cyclocarbons and large carbon clusters, nanobelts and nanoribbons, liquid, metallic, semiconductive and superhard carbons, which could exist under high or low pressures. These carbon allotropes can contain C atoms in the same hybridization state or be as their mixture, for example sp2+sp3. For several carbon allotropes, possible synthesis methods, properties and applications are proposed.
