Hydrogen storage and purification processes represent two key steps in hydrogen fuel production and supply chain, and for this reason they have a critical role in the development of the hydrogen economy. On one hand, the use of carbon membranes can help to overcome some disadvantages of the already commercial techniques adopted for hydrogen separation and purification (such as pressure swing adsorption and fractional/cryogenic distillation). On the other hand, hydrogen storage improvements are necessary for the commercialization of fuel cell cars. Four methods are available for hydrogen storage: liquefaction, compression, storage under chemical bonds, and storage under physical bonds. Carbon nanotubes (CNTs) have been considered, since the end of the 1990s, as interesting materials to adsorb hydrogen, but over time many criticalities have emerged. This chapter takes into account practical applications of CNTs for both processes: separation and storage. CNTs structure is analyzed, together with the main physical and chemical mechanisms that can be used for H2 separation and adsorption.