Hydrogen storage in nanoporous materials can be increased by hydrogen spillover from a supported catalyst to the high-surface area support. The process increases the active temperature of adsorption to the nanoporous support, typically to moderate temperatures (i.e. 300K). The overall surface coverage of hydrogen can be optimized by enhancing the rate of spillover from the catalyst to the nanoporous support and/or increasing the binding energy of atomic hydrogen to specialized surface binding sites. The pressure dependence of hydrogen spillover, the effect of surface chemistry, porosity, metal-support interface, and catalyst loading will be discussed. New results using carbide-derived-carbons, tailored activated carbons, and metal-organic frameworks will be discussed.