A review is presented on the technology, thermodynamics, applications and economics of absorption cycles such as refrigeration, heat pumps and temperature amplifiers; single and multistage cycles, and systems into which they are integrated such asCHP. From this present situation the fundamental thermodynamics of ideal absorption refrigeration is established for single, double and multistage cycles. An exergy analysis is used to prove this theory. The ideal absorption cycle theory is developed to cover absorption heat pumps, cooling with heat recovery, temperature amplifiers and hybrid systems incorporating vapour compression and absorption machines. Having proved absorption cycles to be comprised of Carnot cycles (direct and reverse), this theory was then merged with Carnot driving and cooling cycles' theory to establish a universal law of cold generation cycles. These are combinations of driving and cooling cycles for which the main pmpose is to produce cooling from a combustion driven cycle. The applications and economic evaluations of real direct fired absorption chillers, cold generation systems and the application of absorption chillers to combined heat and power (CHP) systems are analysed. Direct fired chillers have been proved to be economically feasible. The analysis of cold generation cycles indicated the feasibility of certain plant configurations. For the CHP analysis, the exergy costing method was seen to be the most appropriate one for determining the most cost effective application. A review of thermoeconomics applied to an air conditioning system with absorption and CHP is presented. Thermoeconomics was shown to be an appropriate method for optimising systems where absorption cycles are applied. Finally theoretical, practical and economic conclusions are presented regarding the equivalence of vapour compression and absorption cycles.