Résumé
I review recent progress on some non-rational conformal field theories, which were mostly obtained by the conformal bootstrap method. In particular I focus on the sl3 conformal Toda theory, which has a W3 symmetry algebra, and on the H3+ model, which has an affine sl2 symmetry algebra. Both theories are compared to Liouville theory, whose solution is now well-known. I the process I explain why non-rational theories with W3 or affine sl3 symmetries were not fully solved yet, in contrast to Liouville theory and the H3+ model. I also discuss some other sl2-related conformal field theories with string theory motivations, which have not yet been solved but are expected to be solvable.