The limited supply of fossil fuels, its adverse effect on the environment, and growing worldwide demand for energy has necessitated the search for new and clean sources of energy. Hydrogen has been long recognized as a potential solution to meet the world’s energy needs. It has a higher energy per unit mass and is environmentally friendly when used as an energy source with oxygen, providing water as a byproduct. Although hydrogen is most abundantly present on the earth’s surface, it is chemically tied with oxygen as water or in various forms of hydrocarbons. Extraction of this abundant energy source and its use present numerous technological challenges including the development of new and advanced materials to safely store large quantities of hydrogen and deliver them on demand. There are different ways to store hydrogen. Among the well-established high-pressure cylinders for laboratory applications and the liquid hydrogen for air and space applications, metal and complex hydrides including carbon-based materials offer a very safe and efficient way to store hydrogen. Scientific research and technical developments in this area show a wide variation of results. Problems and challenges in this critical area will be reviewed.