Recent developments in hydrogen interaction with carbonaceous materials are reviewed in this article. The interaction is based on van der Waals attractive forces (physisorption), or the overlap of the highest occupied molecular orbitals of carbon with the hydrogen electron, overcoming the activation-energy barrier for hydrogen dissociation (chemisorption). While the physisorption of hydrogen limits the hydrogen-to-carbon ratio to less than one hydrogen atom per two carbon atoms (i.e., 4.2 mass%), in chemisorption, a ratio of two hydrogen atoms per one carbon atom is realized (e.g., in polyethylene). However, the materials with large hydrogen-to-carbon ratios only liberate the hydrogen at elevated temperature. No evidence, apart from theoretical calculations, was found for a new hydrogen-adsorption phenomenon on carbon nanotubes (CNTs), as compared with high-surface-area graphite. The curvature of CNTs and fullerenes increases the reactivity of these materials with hydrogen and leads more easily to the formation of hydrocarbons, as compared with graphite. Nanocrystalline or amorphous carbon exhibits an intermediate state for hydrogen between physisorption and chemisorption and absorbs up to one hydrogen atom per carbon atom. Nanostructured carbonaceous and metallic materials offer a large potential for hydrogen storage and must therefore be investigated in more detail.