Seniority in quantum many-body systems

The use of the seniority quantum number in many‐body systems is reviewed. A brief summary is given of its introduction by Racah in the context of atomic spectroscopy. Several extensions of Racah’s original idea are discussed: seniority for identical nucleons in a single‐j shell, its extension to the case of many, non‐degenerate j shells and to systems with neutrons and protons. To illustrate its usefulness to this day, a recent application of seniority is presented in Bose‐Einstein condensates of atoms with spin.