The energy demand for traditional vapor-compressed technology for space cooling continues to soar year after year due to global warming and the increasing human population's need to improve living and working conditions. Thus, there is a growing demand for eco-friendly technologies that use sustainable or waste energy resources. This review discusses the properties of various refrigerants used for adsorption cooling applications followed by a brief discussion on the thermodynamic cycle. Next, sorbents traditionally used for cooling are reviewed to emphasize the need for advanced capture materials with superior properties to improve refrigerant sorption. The remainder of the review focus on studies using engineered nanoporous frameworks (ENFs) with various refrigerants for adsorption cooling applications. The effects of the various factors that play a role in ENF-refrigerant pair selection, including pore structure/dimension/shape, morphology, open-metal sites, pore chemistry and possible presence of defects, are reviewed. Next, in-depth insights into the sorbent-refrigerant interaction, and pore filling mechanism gained through a combination of characterization techniques and computational modeling are discussed. Finally, we outline the challenges and opportunities related to using ENFs for adsorption cooling applications and provide our views on the future of this technology.