Hydrogen storage has been studied in a large variety of activated carbons and activated carbon fibers and a wide range of pressures (up to 70 MPa). The experimental technique used has good reliability, and the experiments performed have a small error and high reproducibility. This seems to be essential to get trustworthy conclusions. In these samples, we have not found large amounts of hydrogen adsorbed. In any case, an activated carbon derived through a simple preparation method provides hydrogen storage values at 10 MPa close to 1 wt % (i.e., a value close to the target from an application point of view). The experimental results have been compared with theoretical work found in the literature, and an important agreement can be observed. From this study, we conclude that the optimum pore size for hydrogen storage is that which can hold two layers of adsorbed hydrogen. This work also considers practical aspects related to hydrogen storage in activated carbons and activated carbon fibers.