The main goal of this work is to search for new stable porous carbon-based materials, which have the ability to accommodate and store hydrogen gas. Theoretical and experimental studies suggest a close relation between the nano-scale structure of the material and its storage capacity. In order to design materials with a high storage capacity, a compromise between the size and the shape of the nanopores must be considered. Therefore, a number of different carbon-based materials have been investigated: carbon foams, dislocated graphite, graphite intercalated by C60 molecules, and metal-organic frameworks. The structures of interest include experimentally well-known as well as hypothetical systems. The studies were focused on the determination of important properties and special features, which may result in high storage capacities. Although the variety of possible pure carbon structures and metal-organic frameworks is almost infinite, the materials described in this work possess the main structural characteristics, which are important for gas storage.