Information Causality as a physical principle

It is known that the physical principle of ``no-signaling'' alone does not single out quantum correlations, and that the post-quantum no-signaling correlations share many of the features that are supposed to define quantum physics (intrinsic randomness, no-cloning, violation of Bell's inequalities...). This talk focuses on the principle of Information Causality (IC), which generalizes no-signaling and has been proved to come close to singling out quantum correlations. I shall review the successes of IC and also the difficulties that the subsequent research is meeting. In particular, I shall emphasize how a generalization of the initial bipartite scenario to a multipartite one is a most urgent necessary step.