Hydrogen is emerging as a clean energy carrier in the global transition toward decarbonized energy systems. Leveraging established subsurface engineering expertise, underground hydrogen storage can be realized in salt caverns, depleted hydrocarbon reservoirs, and deep saline aquifers. However, the physicochemical characteristics of hydrogen including low viscosity, high diffusivity and strong chemical reactivity create unique challenges for its containment, transport and recovery from porous media. This review systematically analyzes the known interfacial and pore-scale mechanisms governing hydrogen migration, trapping and loss in heterogeneous reservoirs. The key processes comprise capillary trapping, molecular diffusion, interfacial reactions, and microbial activity. Interactions among hydrogen, brine and mineral surfaces are evaluated in terms of wettability, interfacial tension and pore connectivity, all of which directly influence storage efficiency and recovery performance. Advanced experimental methods such as nuclear magnetic resonance, microfluidics models, and X-ray computed tomography, combined with pore-scale simulations, are assessed for their ability to characterize multiphase flow and reactive transport behavior. Furthermore, the impact of operational factors like cushion gas composition, pressure cycling and injection-production strategies on storage integrity is discussed. Addressing these multi-physics and multi-scale challenges is essential for the safe and efficient implementation of underground hydrogen storage. Finally, this review identifies priority research directions aimed at improving mechanistic predictions and optimizing the operational management of hydrogen behavior in subsurface environments.