Topology optimization is proving to be a valuable design tool for physical systems, especially for structural systems. However, its application in the field of heat transfer is less evident but is constantly progressing. In this chapter, we would like to introduce topology optimization in the context of heat exchanger design to the general reader. We also provide a chronological review of available literature to see the current progress of topology optimization in the field of heat transfer and heat exchanger design. We expect that topology optimization will prove to be a valuable tool in heat exchanger design for the coming years.