An interesting connection has recently been found between quantum integrable systems and conformal blocks. In this talk, I will extend this connection in several directions. After a brief introduction to conformal blocks, I will demonstrate that the action of the quartic conformal Casimir operator on d-dimensional scalar conformal blocks can be expressed in terms of certain combinations of commuting integrals of motion of the two particle hyperbolic BC2 Calogero-Sutherland system. Next, I will show that the scalar superconformal blocks in SCFTs with four and eight supercharges can also be identified with the eigenfunctions of the same C-S system. I will also discuss the so-called “seed” conformal blocks used for constructing four-point functions for operators with arbitrary space-time spins in 4d CFTs, before concluding with discussions of possible extensions and work in progress.