A review of various contributions of first principles calculations in the area of hydrogen storage, particularly for the carbon-based sorption materials, is presented. Carbon-based sorption materials are considered as promising hydrogen storage media due to their light weight and large surface area. Depending upon the hybridization state of carbon, these materials can bind the hydrogen via various mechanisms, including physisorption, Kubas and chemical bonding. While attractive binding energy range of Kubas bonding has led to design of several promising storage systems, in reality the experiments remain very few due to materials design challenges that are yet to be overcome. Finally, we will discuss the spillover process, which deals with the catalytic chemisorption of hydrogen, and arguably is the most promising approach for reversibly storing hydrogen under ambient conditions.