Energy storage is considered to be key element in energy supply in the 21st century. This is mainly because it can increase the use of renewable energy sources, improve network stability and the efficiency of energy systems, and reduce the impact of energy production on the environment, especially the impact of fossil fuels. Underground hydrogen storage does not differ significantly from underground natural gas storage. The specific properties of hydrogen gas, its high permeability and negative impact on the properties of exposed steel alloys, mean that it will have to be handled appropriately to ensure impermeability during storage and transport. The selection of geological structures for underground hydrogen storage should be based on a detailed geological analysis that includes an assessment of their usability, storage capacity, long-term storage safety and other factors, both on a global scale and on a regional scale. The ability of hydrogen to “escape” and migrate beyond storage boundaries should be a crucial criterion for selecting suitable storage sites. In this type of storage, the priority is to meet the geological criteria, and only then do we consider other factors (hydrogen production, its transport and injection, costs and profits). Underground hydrogen storage is not yet available nor is it a technically feasible way to store energy. Reducing the cost of hydrogen production by electrolysis in the future will be a decisive factor for the implementation of this method of energy storage on an industrial scale.