This review systemizes the results of research done over the last decade to study the feasibility of the construction and use of solid-state hydrogen accumulators. Consideration has been given to nanoporous carbon and metal-organic framework structures, complex hydrides and nanoporous materials that were created by the authors of this review using radiation-induced methods. It has been shown that the structures that adsorb hydrogen adhering to a mechanism either of physical or chemical adsorption can accumulate it in a sufficient amount, but are not capable of desorbing it in the temperature range required by DOE [1]. It is asserted that the prospects for the creation of hydrogen absorbers with performances acceptable for the practical application are viewed from the standpoint of the development of structures capable of adsorbing hydrogen both in its molecular and atomic states. The authors give the results of their recent research; these show that nanocrystalline materials containing nanopores in their intergranular junctions can adsorb huge amount of hydrogen adhering to the mechanism of both physical and chemical adsorption.