This is a broad and comprehensive review of the development of the concept of exergy and of its application to the analysis and optimization of energy conversion systems. After a brief recapitulation of the basic concepts and a short historical outline, Second-Law Analysis, Thermo-Economics and Exergo-Economics are discussed. In conclusion, an original method developed by the author (Extended Exergy Accounting) is presented and discussed. Copyright © 2005 John Wiley & Sons, Ltd.