Desulfurization of natural gas is achieved commercially by absorption with liquid amine solutions. Adsorption technology could potentially replace the solvent extraction process, particularly for the emerging shale gas wells with production rates that are generally lower than that from the large conventional reservoirs, if a superior adsorbent (sorbent) is developed. In this review, we focus our discussion on three types of sorbents: metal-oxide based sorbents, Cu/Ag-based and other commercial sorbents, and amine-grafted silicas. The advantages and disadvantages of each type are analyzed. Possible approaches for future developments to further improve these sorbents are suggested, particularly for the most promising amine-grafted silicas.