Abstract: There are 2 combinatorial structures intimately connected with the classification of conformal field theories. I'll give their simple definition, review what's known, and state some (possibly disturbing) curiousities. The classification of CFTs is interesting for its own sake, and also because of the remarkable variety of its points-of-contact with other areas of math (A-D-E, Fermat, subfactors, vertex operator algebras,...).