Underground hydrogen storage has emerged as a pivotal component of the low-carbon energy transition, providing a viable solution to the intermittency of renewable energy sources. The distinctive physical and chemical properties of hydrogen, together with its interactions with surrounding rocks and fluids, introduce unique challenges for subsurface storage. This perspective presents recent advances in experimental and modeling efforts of underground hydrogen storage from a multi-scale perspective, highlighting that established methods from hydrocarbon recovery and carbon dioxide storage remain valuable for studying hydrogen systems, yet effectively translating and scaling the relevant physical processes requires renewed attention. Improving the purity and recovery efficiency of stored hydrogen will be central to guiding future reseach on hydrogen storage in geological porous media.