The use of hydrogen as a fuel, the basis of a potential Hydrogen Economy, is currently limited due to a lack of progress in developing suitable storage and delivery systems. Materials that can store hydrogen in large quantities are therefore urgently needed before such an economy can be realized in the future. Carbon nanotubes can have a high hydrogen storage capacity due to their high surface area and capillarity. I provide a brief background of the issues associated with hydrogen storage in carbon nanostructures in this short talk. It is based on the paper "Hydrogen Storage in Carbon Nanostructures: Possibilities and Challenges for Fundamental Molecular Simulations" by S. Banerjee, S. Murad and I. K. Puri that was published in the Proceedings of the IEEE (Vol. 94, pp. 1806-1814, 2006). Listeners will also hear a description of how molecular simulations can be conducted.