Subsurface geological formations provide giant capacities for storing not only greenhouse gases (e.g. carbon dioxide) but also renewable energy, when it is converted into green gas (e.g., hydrogen) or compressed and hot fluids. While the utilisations of subsurface formations for greenhouse gas storage have extensively studied in the past decades, their successful contribution for cyclic green energy storage comes with new scientific challenges too. Hydrogen is expected not only to be stored safely, but to be reclaimed efficiently and with the same purity as in the injection phase. The critical stress also will impose restrictions on the volume, rate, and frequency of the storage cycles. In this talk, I will present the recent advancements from laboratory characterization to pore-scale and reservoir-scale modelling of hydrogen storage; built on our gained knowledge from CO2 storage projects.