The conformal bootstrap programme relies on the expansion of 4-point functions into kinematically determined conformal blocks. I will explain that conformal blocks of scalar 4-point functions in a d-dimensional conformal field theory can mapped to eigenfunctions of a 2-particle hyperbolic Calogero-Sutherland Hamiltonian. The link makes considerable mathematical developments in integrability and the modern theory of special functions available for conformal field theory.