Carbon materials such as graphene, carbon nanotubes, fullerene, and graphene nanoflakes (GNFs) are used for hydrogen storage. The doping of alkali metals to these materials generally increases the accumulation density of molecular hydrogen (H2). However, the reason why the doping enhances the ability of the H2 storage of GNF is not clearly known, although there are some explanations. In addition, the information on the storage capacity of GNF is ambiguous. In the present review article, we introduce our recent theoretical studies on the interaction of GNF with H2 molecules carried out to elucidate the mechanism of hydrogen storage in alkali-doped GNFs. As alkali metals, lithium (Li), sodium (Na), and potassium (K) were examined, and the abilities of hydrogen storage were discussed. Next, the mechanism of Li-diffusion on GNF, which plays a crucial role in Li-battery, was presented. There are several unanswered questions. In particular, does lithium diffuse randomly on GNF? Or is there a specific diffusion path? We present our study, which elucidates the factors governing lithium diffusion on GNF. If the dominant factor is known, it is possible to arbitrarily control the diffusion path of lithium. This will lead to the development of highly functional battery materials. Finally, the molecular design of H adsorption–desorption reversible storage devices based on GNF will be introduced. Elucidating the mechanism of hydrogen storage, Li-diffusion on GNF, and molecular design of storage device is important in understanding the current molecular devices and provide a deeper insight into materials chemistry.