Cancellation of chiral anomalies played a crucial role in the emergence of string theory in the eighties of last century.
Initially, seemingly mysterious cancellations where found in field theories related to string theory. It was clear that these
numerical coincidences had to be related to a deep property of closed string theory called "modular invariance". The direct relation was made clear a few years later when Nick Warner and I constructed a anomaly generating function that a little bit later became known as "the elliptic genus". In the second part of the talk I will discuss an application to the classification of meromorphic conformal field theories, which are additional items on a list that includes the famous "Monster Module".
