Hydrogen is a promising energy carrier in future energy systems. However, storage of hydrogen is a substantial challenge, especially for applications in vehicles with fuel cells that use proton-exchange membranes (PEMs). Different methods for hydrogen storage are discussed, including high-pressure and cryogenic-liquid storage, adsorptive storage on high-surface-area adsorbents, chemical storage in metal hydrides and complex hydrides, and storage in boranes. For the latter chemical solutions, reversible options and hydrolytic release of hydrogen with off-board regeneration are both possible. Reforming of liquid hydrogen-containing compounds is also a possible means of hydrogen generation. The advantages and disadvantages of the different systems are compared.