Conformal bootstrap programme in the spacetime dimensions d>2 has seen a revival in the last decade. I will describe a direct connection between the important constituents of the bootstrap method, conformal blocks, and the Calogero-Sutherland-type integrable models. It goes via harmonic analysis on the conformal group and paves the way for using double affine Hecke algebras and the related theory of special functions in the study of conformal field theories.