Rational conformal field theories (RCFTs) possess a finite number of primaries with respect to their chiral algebra. As a consequence, their four point functions decompose as finite sums of products of holomorphic and antiholomorphic conformal blocks. In this talk we will see that conformal blocks can be expressed as components of vector-valued modular forms, which often can be easily computed based on minimal information about the RCFT. We will also find a surprising correspondence by which, for some families of RCFTs, some conformal blocks coincide with the characters of an associated torus RCFT. This talk is based on an upcoming paper with Miranda Cheng and Terry Gannon.