One of the limitations to the widespread use of hydrogen as an energy carrier is its storage in a safe and compact form. Herein, recent developments in effective high-capacity hydrogen storage materials are reviewed, with a special emphasis on light compounds, including those based on organic porous structures, boron, nitrogen, and aluminum. These elements and their related compounds hold the promise of high, reversible, and practical hydrogen storage capacity for mobile applications, including vehicles and portable power equipment, but also for the large scale and distributed storage of energy for stationary applications. Current understanding of the fundamental principles that govern the interaction of hydrogen with these light compounds is summarized, as well as basic strategies to meet practical targets of hydrogen uptake and release. The limitation of these strategies and current understanding is also discussed and new directions proposed.