Luca Salasnich Review on 'Integrability of the S-Matrix vs Integrability of the Hamiltonian' by C. Jung and T.H. Seligman (4K, Latex) ABSTRACT. We review the paper 'Integrability of the S-Matrix vs Integrability of the Hamiltonian' by C. Jung and T.H. Seligman (Phys. Rep. {\bf 285}, 77-141 (1997)). This paper deals with the connection between the integrability of the scattering matrix $S$ and the integrability of the Hamiltonian $H$ for classical and quantum Hamiltonian systems. (To be published in Mathematical Reviews).