Solar heating and cooling (SHC) systems are currently under rapid development and deployment due to their potential to reduce fossil fuel use and to alleviate greenhouse gas emissions in the building sector a sector which is responsible for 40% of the world energy use. The available technologies on the market for thermally driven cooling systems are absorption and adsorption chillers, solid and liquid desiccant cooling systems, and ejector refrigeration cycles. Of these, absorption chillers are considered as the most desirable method for harnessing solar thermal energy due to their relative maturity, reliability, and higher efficiency. In addition, absorption chillers can take advantage of economies of scale in large buildings to obtain a relatively good levelized cost of cooling as compared to other thermally-driven air-conditioning systems. In this paper, the background theory on solar-powered absorption chillers is presented followed by a comprehensive literature review of the recent existing theoretical and experimental investigations on this technology is conducted. The review shows that the majority of solar absorption chillers installed and much of the research around the world is based on single-effect chillers and low-temperature solar thermal collectors, while less emphasis has been placed on the combination of high-temperature solar thermal collectors and multi-effect absorption chillers, especially triple effect chillers. Research studies indicate the use of gas-fired backup systems for single-effect chillers is inefficient due to its very low primary energy savings. It was also found that the storage tank and piping can be major sources of heat losses in solar absorption cooling systems. Thus, special care should be taken to ensure sufficient and appropriate insulation for all heat loss components. In regions with low direct normal incidence solar resources (e.g. most of Europe), solar multi-effect chillers are relatively inefficient, so single-effect chiller-based solar cooling systems are the best techno-economic choice in such regions. Conversely, multi-effect absorption chillers with high-temperature collectors are indeed promising in regions with high solar resources. However, the review shows that using currently available technology, SHC absorption chillers are not able to economically compete with conventional cooling without government subsidies and incentives. Therefore, improving the economic performance of these systems is essential. While there is clearly more that can be done on chiller and solar collector components themselves, we believe some R&D emphasis going forward should also be dedicated to the balance of the system, including optimization of the system configuration, minimizing parasitic losses, improved design and integration of thermal storage and auxiliary system, and numerous controls and operational aspects. To date, many of these topics have been largely overlooked in favor of chiller performance studies.