This paper provides a critical review of the literature on heat-exchanger network synthesis, the most commonly studied problem in process synthesis. After a review of solution methods, we present the chronological milestones in the development of the field and we discuss separately each of 461 related works leading up to the turn of the century. Then, we present several classification schemes of this body of work based on a number of modeling and algorithmic criteria. Finally, we offer a critical assessment of the current status of research in this area and provide suggestions for future research.