The paper adopts an interdisciplinary approach to comprehensively review the current knowledge in the field of porous geological materials for hydrogen adsorption. It focuses on detailed analyses of the adsorption characteristics of hydrogen in clay minerals, shale, and coal, considering the effect of factors such as pore structure and competitive adsorption with multiple gases. The fundamental principles underlying physically controlled hydrogen storage mechanisms in these porous matrices are explored. The findings show that the adsorption of hydrogen in clay minerals, shale, and coal is predominantly governed by physical adsorption that follows the Langmuir adsorption equation. The adsorption capacity decreases with increasing temperature and increases with increasing pressure. The presence of carbon dioxide and methane affects the adsorption of hydrogen. Pore characteristics—including specific surface area, micropore volume, and pore size—in clay minerals, shale, and coal are crucial factors that influence the adsorption capacity of hydrogen. Micropores play a significant role, allowing hydrogen molecules to interact with multiple pore walls, leading to increased adsorption enthalpy. This comprehensive review provides insights into the hydrogen storage potential of porous geological materials, laying the groundwork for further research and the development of efficient and sustainable hydrogen storage solutions.