Calogero models comprise several integrable systems in classical mechanics and their relatives; they are describing interacting systems of particles on a circle or on a line. Basic variants include Calogero-Moser system, Calogero-Sutherland system and “relativistic” Ruijsenaars model?s. Calogero-Moser system was a historical source of the study of Dunkl operators and Cherednik’s double Hecke algebras. The Calogero-Moser system can also be related to the rational -soliton solutions of rational KP equation; the elucidation of the relation between the soliton solutions and solutions of the Calogero-Moser system is rather deep and is called Calogero-Moser correspondence. Its modern formulation involves noncommutative algebraic geometry.
Some special functions come out of analysis of Calogero models, like Jack polynomials.
Pavel Etingof, Lectures on Calogero-Moser systems, pdf