Hydrogen storage by physisorption is a very promising technique due to its fast kinetics and full reversibility. The key to reach high storage capacities is high specific surface area. Extremely large surface areas can only be achieved by materials with high porosity, i.e., nanosponges like MOF-177 (4239 m2 g−1) and DUT-23(Co) (4850 m2 g−1). Even specific surface areas of more than 6000 m2 g−1 have been recently reported in the literature and these new materials reach hydrogen excess uptakes up to 9 wt% at 77 K. Within the novel class of metal–organic frameworks (MOFs), crystalline materials can be synthesized with well-defined pore structure and inner surface areas exceeding the best activated carbons. An overview is given on adsorption and desorption measurements performed mainly in our laboratory. The focus of this paper lies on the progress achieved in understanding the structure–property relationship of hydrogen adsorption in nanosponges. Furthermore, technologically relevant parameters as total and usable capacities are introduced.