Metal-organic polyhedra (MOPs), are discrete metal-organic molecular assemblies. They are useful as host molecules that can provide tailorable internal volume in terms of metrics, functionality, and active metal sites. As a result, these materials are potentially useful for a variety of applications, such as highly selective guest inclusion and gas storage, and as nanoscale reaction vessels. This review identifies the nine most important polyhedra, and describes the design principles for the five polyhedra most likely to result from the assembly of secondary building units, and provides examples of these shapes that are known as metal-organic crystals.