With the rapid growth in demand for effective and renewable energy, the hydrogen era has begun. To meet commercial requirements, efficient hydrogen storage techniques are required. So far, four techniques have been suggested for hydrogen storage: compressed storage, hydrogen liquefaction, chemical absorption, and physical adsorption. Currently, high-pressure compressed tanks are used in the industry; however, certain limitations such as high costs, safety concerns, undesirable amounts of occupied space, and low storage capacities are still challenges. Physical hydrogen adsorption is one of the most promising techniques; it uses porous adsorbents, which have material benefits such as low costs, high storage densities, and fast charging–discharging kinetics. During adsorption on material surfaces, hydrogen molecules weakly adsorb at the surface of adsorbents via long-range dispersion forces. The largest challenge in the hydrogen era is the development of progressive materials for efficient hydrogen storage. In designing efficient adsorbents, understanding interfacial interactions between hydrogen molecules and porous material surfaces is important. In this review, we briefly summarize a hydrogen storage technique based on US DOE classifications and examine hydrogen storage targets for feasible commercialization. We also address recent trends in the development of hydrogen storage materials. Lastly, we propose spillover mechanisms for efficient hydrogen storage using solid-state adsorbents.