•Using solar concentrating collectors in refrigeration is reviewed and discussed.•The focus is on solar-driven absorption and adsorption refrigeration cycles.•Compound parabolic, trough, dish, and linear Fresnel collectors are considered.•Parabolic trough collector is dominant, among concentrating collectors.•Absorption refrigeration has been reported much more than the adsorption. Considering the operating temperatures, there is a reasonable match between solar concentrating collectors and some thermal-powered cooling technologies. Both current and previous studies demonstrate that concentrating solar collectors have had a significant impact on the development of solar absorption and adsorption refrigeration technologies. Therefore, studying of sorption refrigeration, integrated with solar concentrating collectors, could be an important issue. On this basis, this paper is undertaken to present a detailed review of solar refrigeration, with a specific focus on the absorption and adsorption cooling cycles, driven by solar concentrating collectors, aiming for providing a comprehensive guideline for the future studies in this field. This review article is divided into four main sections, each of which presents the methods, results, and analyses, relating to the studies in the field of cooling systems powered by concentrating collectors. These four main contents include parabolic trough, compound parabolic, dish, and linear Fresnel collectors for refrigeration purposes, either direct or indirect. The thermodynamic properties of the related refrigeration cycles are reviewed and analyzed. As a general conclusion, a solar sorption refrigeration could be competitive with the conventional coolers, if a suitable combination of working fluid, solar collector, and refrigeration subsystems would be selected. The present study could provide the possibility of an appropriate selecting of the solar cooling sub-systems for future studies. Finally, it is worth mentioning that there is more need for further research works on the solar-based absorption refrigeration cycles, to make them more economic and more efficient.