Biogas is a vital energy source in establishing a sustainable society, based on the principles of a circular economy. Nevertheless, effective biogas upgrading steps, particularly for hydrogen sulfide (H2S) removal, are required to ensure its applicability to the industrial fields. This is because most downstream applications (except turbines) require H2S concentrations to be at 1000 ppm and below to minimize corrosion to the piping and facilities. Hence, to date, several approaches (e.g., scrubbing, green solvents, adsorption, and membranes) have been employed to eliminate H2S. Comparatively, adsorption and membrane separation technologies showcase advantages as the process can be performed without phase change and secondary pollutants, thus increasing the practical feasibility in real operations. In this review, performance analyses of adsorption and membrane based on reported data will be conducted, followed by the outlook of these two technologies from the standpoint of techno-economic feasibility and circular economy. © 2024 The Institution of Chemical Engineers