Metal-organic frameworks (MOFs) are a new class of porous materials that can store high amounts of molecular hydrogen via physisorption owing to their large specific surface area and ultra-high porosity. The adsorption has fast kinetics and is fully reversible, however, high storage capacities can only be reached at cryogenic conditions due to the low heat of adsorption. A thorough characterization allows to correlate the adsorption properties to the structure of the materials.