Hydrogen adsorption and storage using solid-state materials is an area of much current research interest, and one of the major stumbling blocks in realizing the hydrogen economy. However, no material yet researched comes close to reaching the DOE 2015 targets of 9 wt% and 80 kg m−3 at this time. To increase the physisorption capacities of these materials, the heats of adsorption must be increased to ∼20 kJ mol−1. This can be accomplished by optimizing the material structure, creating more active species on the surface, or improving the interaction of the surface with hydrogen. The main focus of this progress report are recent advances in physisorption materials exhibiting higher heats of adsorption and better hydrogen adsorption at room temperature based on exploiting the Kubas model for hydrogen binding: (η2-H2)–metal interaction. Both computational approaches and synthetic achievements will be discussed. Materials exploiting the Kubas interaction represent a median on the continuum between metal hydrides and physisorption materials, and are becoming increasingly important as researchers learn more about their applications to hydrogen storage problems.