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A brief and incomplete review of known integrable and(quasi)-exactly-solvable quantum models with rational (meromorphic in Cartesiancoordinates) potentials is given. All of them are characterized by (i) adiscrete symmetry of the Hamiltonian, (ii) a number of polynomialeigenfunctions, (iii) a factorization property for eigenfunctions, and admit(iv) the separation of the radial coordinate and, hence, the existence of the2nd order integral, (v) an algebraic form in invariants of a discrete symmetrygroup (in space of orbits).

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