Résumé : We‘ll introduce two models of 2 dimensional conformal field theory with respective central charges c>25 and c<1, defined using probabilistic methods. These models satisfy the gluing Segal axioms and we’ll explain how to uncover the integrability of the theory, via the bootstrap method, and how to define the conformal blocks of the theory starting from probabilistic expectations and combining with spectral methods. This is is based on several joint works with Kupiainen, Rhodes, Vargas and Baverez.