Aspects of anomalies in field theory

We discuss some formal aspects of quantum anomalies with an emphasis on the regularization of field theory. We briefly review how ambiguities in perturbation theory have been resolved by various regularization schemes. To single out the true quantum anomaly among ambiguities, the combined ideas of PCAC, soft pion limit and renormalizability were essential. As for the formal treatment of quantum anomalies, we mainly discuss the path integral formulation both in continuum and lattice theories. In particular, we discuss in some detail the recent development in the treatment of chiral anomalies in lattice gauge theory.