The inadequate fossil fuel resources and their impacts on the global environment are the reason for the inclination of researchers to improve clean energy technologies. Using fuel cells, the chemical energy can directly transform into electrical energy with high efficacy. Hydrogen is the most ensuring alternative for fossil fuel, but its storage is a prime issue. This chapter overviews hydrogen storage studies on a series of molecules, cages, and clusters. We describe how the nature of binding between hydrogen molecule and storage materials impact the absorption and desorption properties. We then discuss explicit examples of various hydrogen storage materials and their hydrogen storage capacities.