Modular functor is a categorical concept that captures essential properties of conformal blocks. Surprisingly, from the interpretation of the family of conformal blocks as a modular functor, we learn that a certain category of representations of an affine Lie algebra has a structure of modular tensor category. I will explain how these work after covering prerequisites on both conformal blocks and modular tensor categories. (This is an extended version of my final presentation in the conformal blocks course last semester.)