The removal of the environmentally toxic and corrosive hydrogen sulfide (H2S) from gas streams with varying overall pressure and H2S concentration is a long-standing challenge faced by the oil and gas industries. The present work focuses on H2S capture using a relatively new type of material, namely metal-organic frameworks (MOFs), in an effort to shed light on their potential as adsorbents in the field of gas storage and separation. MOFs hold great promise as they make possible the design of structures from organic and inorganic units, but also as they have provided an answer to a long-term challenging objective, i.e., how to design extended structures of materials. Moreover, in designing MOFs, one may functionalize the organic units and thus, in essence, create pores with different functionalities, and also to expand the pores in order to increase pore openings. The work presented herein provides a detailed discussion, by thoroughly combining the existing literature on new developments in MOFs for H2S removal, and tries to provide insight into new areas for further research.