Hot isostatic pressing (hipping) can be used for upgrading castings, densifying presintered components, consolidating powders, and interfacial bonding. It involves the simultaneous application of a high pressure and elevated temperature in a specially constructed vessel. The pressure is applied with a gas (usually inert) and, so, is isostatic. Under these conditions of heat and pressure, internal pores or defects within a solid body collapse and diffusion bond. Encapsulated powder and sintered components alike are densified to give improved mechanical properties and a reduction in the scatter band of properties. In this article, the basic science of sintering and hipping is summarized and contrasted. The current state of understanding and modeling of hipping is then reviewed. Models can be classified either as microscopic or macroscopic in their approach. In the microscopic approach, the various mechanisms of densification are analyzed in terms of a single particle and its surroundings. In the macroscopic approach, the compact is treated as a continuous medium. In hipping, although the pressure is isostatic, shrinkage is not generally isotropic, particularly if containment is used. However, the shrinkage can now be well predicted, provided that the material and container properties are accurately known.