A sustainable energy economy will be demanding primary energy sources, preferably renewable and mainly domestically available, using energy carriers, such as hydrogen and electricity, able to solve environmental problems and to assure adequate energy security. Instrumental to such goals will be the research and development of storage systems with performance characteristics compatible with major application requirements. Lithium or nickel are replacing lead in batteries, in order to better meet the extremely varying technical and economical requirements in fast growing conventional and new applications. Moreover, few technologies now permit to store hydrogen by modifying its physical state in gaseous or liquid form. The variety of hydrogen needs in the energy systems and in the vehicular sector is justifying the effort on solid state (metal hydrides and carbon nanostructures) or chemical systems (chemical hydrides). In this overview, emphasis is given to the major achievements in the field of electrical energy and hydrogen storage, in relation to the technological goals, which have been proposed in the major public research and collaborative programs throughout the world.