This article is a principle-based review of a growing body of fundamental research that documents the opportunity for optimizing *geometrically* the cooling of spaces (e.g., electronics packages) that generate heat volumetrically. The chief result of geometric optimization is the identification of an optimal internal structure—optimal spacings between components (e.g., plates and fins), optimal sizes and aspect ratios for cooling channels, and optimal frequencies for pulsating flows. The origin of these optimal geometric features—the construction of the system—lies in the global effort to use every infinitesimal volume to the maximum, i.e., to pack the volume not only with the most heat generating components, but also with the ‘most’ coolant, in such a way that every fluid packet is engaged *effectively* in cooling. The optimal aspect ratio for ducts with forced and natural convection corresponds to the special geometry and flow conditions where boundary layers meet just as the coolant exits the channel. This “constructal” design principle is illustrated by several classes of examples: laminar forced and natural convection, and various internal arrangements (parallel plates, staggered plates, cylinders in cross flow, square pins with impinging flow). General trends (scaling laws) of optimal geometric form are revealed by the optimal-structure results, this, in spite of the diversity of the optimized configurations.

*Shape and Structure, from Engineering to Nature*, Cambridge University Press, Cambridge, UK.

*Advances in Thermal Modeling of Electronic Components and Systems*, Vol. 1, eds., A. Bar-Cohen and A. D. Kraus, Hemisphere, New York, pp. 129–282.

*Cooling Technology for Electronic Equipment*, ed., W. Aung, Hemisphere, New York, pp. 195–210.

*Air Cooling Technology for Electronic Equipment*, CRC Press, Boca Raton, FL.

*Convection Heat Transfer*, Wiley, New York, p. 157, problem 11.

*Heat Transfer*, Wiley, New York.