Regularization and Anomalies in Gauge Theory

Some of the basic issues related to the regularization and anomalies in gauge theory are reviewed, with particular emphasis on the recent development in lattice gauge theory. The generalized Pauli-Villars regularization is discussed from a view point of the covariant regularization of currents, and the construction of a regularized effective action in terms of covariant currents is compared with the lattice formulation of chiral Abelian theory.