The classification of RCFT means different things to different people, but the most accessible, and perhaps the prettiest, aspect of it is the classification of modular invariant (torus) partition functions, which tell you the spectrum of the theory. I'll review the progress made recently on this problem, for the case where the chiral algebras come from affine Kac-Moody algebras (the so-called Wess-Zumino-Witten models). I'll also comment on the classification of cyclindrical partition functions (the so-called NIM-reps), which are more directly relevant for the framework of Fuchs-Runkel-Schweigert.