Stirred-tank reactors are used throughout the process industry. They are not only applied in the chemical industry, but also in newer industrial sectors, such as biologics, pharmaceuticals, nanotechnology, and regenerative medicine. Certain features have not changed for many years, but the understanding of the physical processes occurring within has greatly increased. Since knowledge of the interaction between the physics of mixing, single-or multiphase, and the underlying science is critical, the physical processes of mixing/stirring are considered as they developed over the last~75 years.