Removal of hydrogen sulfide (H2S) released from various source processes is crucial because this compound can cause corrosion and environmental damage even at low concentration levels. The porous materials offer a wide variety of chemical architectures with tunable pore size and high surface area that are very promising for the adsorption of H2S molecules. This review attempts to comprehensively compile the current studies in the literature on hydrogen sulfide removal in gas purification processes using highly porous materials such as zeolites, carbon materials, activated carbon, porous metal oxides, mesoporous silica, and metal-organic frameworks as highly effective adsorbents. Possible interactions between the H2S and active adsorption sites of these materials are also discussed. Surface functionality and porosity play a crucial role in the H2S removal performance by virgin or modified porous materials. However, tailoring these materials to obtain high adsorption capacity, good selectivity, and suitable stability and regenerability and to retain structural integrity under high temperatures or in the presence of moisture are still the major challenges in the practical applications. According to the extensive background knowledge for H2S removal by different porous materials in this review, it can be expected that readers will gain insight into the further developments in this area and the design of new cost-effective sorbents.