A classification of commuting rational functions, that is of rational solutions of the functional equation A(X) =X(A), was obtained in the beginning of the past century by Fatou, Julia, and Ritt. In the talk we will present a solution of a more general problem of description of semi-conjugate rational functions, that is of rational solutions of the functional equation A(X) =X(B) in terms of groups acting properly discontinuously on the Riemann sphere or complex plane.