A review with 55 refs. covering theoretical calculations (at 77, 100 and 298 K at 70 bar and 10 MPa) and experiments on physical sorption of H 2 on active macropore C and in nanostructures (pure and metal-doped C nanotubes, C nanofibers), solid state storage involving hydridation of metals and alloys, the hydrogenation-disproportionation-dehydrogenation-recombination cycle, the US DoE Hydrogen Plan, and chemical (reduction of C-60 with Na in liquid NH3 to fulleranes C60Hx, x = 2-36 pressure hydrogenation of C-60 to C60Hx, x = 42, 44, 48, 52, >52, at 700 atm and 700 K) and electrochemical hydrogenation to fullerane C60H48) storage techniques. The data reported are disperse and further studies are indispensable.