Hydrogen sulfide (H₂S) is a flammable, corrosive and lethal gas even at low concentrations (ppm levels). Hence, the capture and removal of H₂S from various emitting sources (such as oil and gas processing facilities, natural emissions, sewage treatment plants, landfills and other industrial plants) is necessary to prevent and mitigate its adverse effects on human (causing respiratory failure and asphyxiation), environment (creating highly flammable and explosive environment), and facilities (resulting in corrosion of industrial equipment and pipelines). In this review, the state-of-the-art technologies for H₂S capture and removal are reviewed and discussed. In particular, the recent technologies for H₂S removal such as membrane, adsorption, absorption and membrane contactor are extensively reviewed. To date, adsorption using metal oxide-based sorbents is by far the most established technology in commercial scale for the fine removal of H₂S, while solvent absorption is also industrially matured for bulk removal of CO₂ and H₂S simultaneously. In addition, the strengths, limitations, technological gaps and way forward for each technology are also outlined. Furthermore, the comparison of established carbon capture technologies in simultaneous and selective removal of H₂S–CO₂ is also comprehensively discussed and presented. It was found that the existing carbon capture technologies are not adequate for the selective removal of H₂S from CO₂ due to their similar characteristics, and thus extensive research is still needed in this area.