This paper deals with a review on exergy analyses of lithium bromide-water based single to triple effect direct and indirect fired vapour absorption systems. The analysis carried out by various investigators on exergy of the absorption cycles have been discussed. To fill the gap in the knowledge on exergy destruction rate in the absorption system, optimization of the single to triple effect direct and indirect fired absorption cycles have been conducted for a wide range of operating conditions. Hence optimum parameters in various components of the systems for maximum exergy coefficient of performance and minimum exergy destruction rate have been determined. The indirect fired systems have been optimized for different temperatures of the energy source related to the main generator temperature. While the direct fired systems have been optimized considering exergy destruction rate during the combustion process of energy sources. The energy sources selected in the present analysis are compressed natural gas and liquefied petroleum gas. Double effect cycle yields better exergy performance when the difference in temperatures of the energy source and the generator is between 6 to 37 degrees C, while triple effect cycle performs well when it is beyond 37 degrees C.