Natural gas, biogas, and refinery gas all include H2S, which has adverse effects not only on the environment and human health but also on the equipment and catalysts that are employed in the relevant processes. H2S is removed from the aforementioned gases using a variety of techniques in order to fulfill the necessary sales criteria and for reasons of safety. The adsorption method stands out among various other approaches due to its straightforward operation, high level of efficiency, and low overall cost. This technique makes use of a variety of adsorbents, such as metal-organic frameworks (MOFs), activated carbon, and zeolites. The use of zeolite-based adsorbents is by far the most common of these various types. This is due to the specific properties of zeolite-based adsorbents, which include a high adsorption capacity, the ability to be regenerated, a high temperature stability, a diversity of types, the possibility of modification, high efficiency, and low cost. In addition, research is being done on adsorbents that are made from inexpensive raw materials in order to remove H2S. This article focuses on zeolites, zeolite modifications, and wastes as an adsorbent for the removal of H2S, all of which have been investigated fruitfully in recent years, as well as the promising applications of zeolites.