This talk will discuss the relation between vertex operator algebras and modular forms. It has been known for a long time that the characters of irreducible integrable highest weight modules for affine Kac-Moody algebras and the characters of irreducible highest weight modules for the minimal series of the Virasoro algebra are modular functions. We will explain, in fact, that this is true for general rational vertex operator algebra. That is, the irreducible characters of any rational vertex operator algebra are modular functions. We also extend this result to include a finite group action
