Anomalies and the Green-Schwarz mechanism

Anomalies are a very powerful tool in constraining theories beyond the standard model. We give a pedagogical overview of some topics illustrating the important role played by spacetime anomalies in string theory. After discussing the general problem of anomaly cancellation in quantum field theory, the focus is set on the cancellation of anomalies in type-I string theory through the Green-Schwarz mechanism. The notion of anomaly inflow is also reviewed, as well as its application to the evaluation of D-brane anomalous couplings. Finally, we briefly comment on recent developments concerning the reformulation of anomalies in the language of category theory.