Anomaly Structure of Supergravity and Anomaly Cancellation

We display the full anomaly structure of supergravity, including new D-term contributions to the conformal anomaly. This expression has the super-Weyl and chiral U(1)_K transformation properties that are required for implementation of the Green-Schwarz mechanism for anomaly cancellation. We outline the procedure for full anomaly cancellation. Our results have implications for effective supergravity theories from the weakly coupled heterotic string theory.