  Conformal blocks are the central ingredient of the conformal bootstrap
programme. We elaborate on our recent observation that uncovered a relation
with wave functions of an integrable Calogero-Sutherland Hamiltonian in order
to develop a systematic theory of conformal blocks. Our main goal here is to
review central ingredients of the Heckman-Opdam theory for scattering states of
Calogero-Sutherland models with special emphasis to the relation with scalar
4-point blocks. We will also discuss a number of direct consequences for
conformal blocks, including a new series expansion for blocks of arbitrary
complex spin and a complete analysis of their poles and residues. Applications
to the Froissart-Gribov formula for conformal field theory, as well as
extensions to spinning blocks and defects are briefly discussed before we
conclude with an outlook on forthcoming work concerning algebraic consequences
of integrability.
