Energy, gases, and solids in underground sites are stored in mining excavations, natural caverns, salt caverns, and in the pore spaces of rock formations. Aquifer formations are mainly isolated aquifers with significant spreading, permeability, and thickness, possessing highly mineralized non-potable waters. This study discusses the most important aspects that determine the storage of natural gas, hydrogen, or carbon dioxide in deep aquifers. In particular, the selection and characterization of the structure chosen for underground storage, the storage capacity, and the safety of the process are considered. The choice of underground sites is made on the basis of the following factors and criteria: geological, technical, economic, environmental, social, political, or administrative–legal. The geological and dynamic model of the storage site is then drawn based on the characteristics of the structure. Another important factor in choosing a structure for the storage of natural gas, hydrogen, or carbon dioxide is its capacity. In addition to the type and dimensions of the structure and the petrophysical parameters of the reservoir rock, the storage capacity is influenced by the properties of the stored gases and the operating parameters of the storage facility. Underground gas storage is a process fraught with natural and technical hazards. Therefore, the geological integrity of the structure under consideration should be documented and verified. This article also presents an analysis of the location and the basic parameters of gas storage and carbon dioxide storage facilities currently operating in underground aquifers. To date, there have been no successful attempts to store hydrogen under analogous conditions. This is mainly due to the parameters of this gas, which are associated with high requirements for its storage.