One of the trends of thermodynamics during the last thirty years has been development of powerful techniques which can optimize complex energy systems taking into account economic factors. These are called methods of thermoeconomic optimization. This paper presents basics of the established methods of thermoeconomics and some of the recent developments. Furthermore application of direct (by differentiation) optimization method to the known irreversible Carnot engine model and the results of this optimization are given, that clarifies the role of the basic thermoeconomic parameters. Copyright © 2005 John Wiley & Sons, Ltd.