The quantum inverse scattering method relates two different approaches: 1. * the Bethe ansatz, a method of solving integrable quantum models in one space and one time dimension; 2. * the Inverse scattering transform, a method of solving classical integrable differential equations of the evolutionary type. The theory of correlation functions was developed: determinant representations, descriptions by differential equations and the Riemann–Hilbert problem. Asymptotics of correlation functions (even for space, time and temperature dependence) were evaluated in 1991.