This paper outlines the fundamentals of the methods of exergy analysis and entropy generation minimization (or thermodynamic optimization—the minimization of exergy destruction). The paper begins with a review of the concept of irreversibility, entropy generation, or exergy destruction. Examples illustrate the accounting for exergy flows and accumulation in closed systems, open systems, heat transfer processes, and power and refrigeration plants. The proportionality between exergy destruction and entropy generation sends the designer in search of improved thermodynamic performance subject to finite-size constraints and specified environmental conditions. Examples are drawn from energy storage systems for sensible heat and latent heat, solar energy, and the generation of maximum power in a power plant model with finite heat transfer surface inventory. It is shown that the physical structure (geometric configuration, topology) of the system springs out of the process of global thermodynamic optimization subject to global constraints. This principle generates structure not only in engineering but also in physics and biology (constructal theory). Copyright © 2002 John Wiley & Sons, Ltd.