The changes in the energy sector after the Paris agreement and the establishment of the Green Deal, pressed the governments to embrace new measures to reduce greenhouse gas emissions. Among them, is the replacement of fossil fuels by renewable energy sources or carbon-neutral alternative means, such as green hydrogen. As the European Commission approved green hydrogen as a clean fuel, the interest in investments and dedicated action plans related to its production and storage has significantly increased. Hydrogen storage is feasible in aboveground infrastructures as well as in underground constructions. Proper geological environments for underground hydrogen storage are porous media and rock cavities. Porous media are separated in depleted hydrocarbon reservoirs and aquifers, while rock cavities are subdivided into hard rock caverns, salt caverns, and abandoned mines. Depending on the storage option, various technological requirements are mandatory, influencing the required capital cost. Although the selection of the optimum storage technology is site depending, the techno-economical appraisal of the available underground storage options featured the porous media as the most economically attractive option. Depleted hydrocarbon reservoirs were of high interest as site characterisation and cavern mining are omitted due to pre-existing infrastructure, followed by aquifers, where hydrogen storage requires a much simpler construction. Research on data analytics and machine learning tools will open avenues for consolidated knowledge of geological storage technologies.