From Quantum $A_N$ (Calogero) to $H_4$ (Rational) Model

A brief and incomplete review of known integrable and (quasi)-exactly-solvable quantum models with rational (meromorphic in Cartesian coordinates) potentials is given. All of them are characterized by $(i)$ a discrete symmetry of the Hamiltonian, $(ii)$ a number of polynomial eigenfunctions, $(iii)$ a factorization property for eigenfunctions, and admit $(iv)$ the separation of the radial coordinate and, hence, the existence of the 2nd order integral, $(v)$ an algebraic form in invariants of a discrete symmetry group (in space of orbits).