We present a path-integral formulation of conformal anomalies and point out an intimate interplay of the local Poincare anomaly and the dilatational anomaly. A key observation in our approach is that the algorithm of the path-integral formulation has natural foundation within the zeta-function regularization scheme. This observation shows us how to treat nonlinear systems as well as higher-order anomalies and suggests a way to understand the Adler-Bardeen theorem for chiral anomalies within the path-integral approach.