Diamond has a unique combination of properties, such as the highest hardness and thermal conductivity among any known material, high electrical resistivity, a large optical band gap, and high transmission. It also offers good resistance to chemical erosion, low adhesion and friction, and an extremely low thermal expansion coefficient. As such, diamond has become a desirable material in a wide range of applications in mechanical, chemical, optical, thermal, and electrical engineering. In many cases, the surface of a diamond component or element must have a superior finish, often down to a surface roughness of nanometers. However, due to its extreme hardness and chemical inertness, polishing diamond and its composites has been a sophisticated process. Polishing of diamond materials will provide a state-of-the-art analysis, both theoretically and experimentally, of the most commonly used polishing materials.