The interaction of hydrogen with carbon nanostructures (nanotubes-CNT, fullerenes) are discussed on the basis of density-functional based tight-binding calculations. The structural and electronic properties of hydrogenated fullerenes (C 6 0 -H) and nanotubes (CNT-H) are described. The adsorption and penetration of molecular hydrogen (H 2 ) through the carbon network of the fullerenes and CNTs is critically examined. It is shown that the penetration of H 2 molecules into these structures is strongly suppressed. Finally, the formation of H-CNT by discharge of hydrogen ions as a possible basic step for an electrochemical-based hydrogen storage in CNTs is discussed.