Anomalies, boundaries and the in-in formalism

In the context of quantum field theory, an anomaly exists when a theory has a classical symmetry which is not a symmetry of the quantum theory. This short exposition aims at introducing a new point of view, which is that the proper setting for anomaly calculations is the `in-in', or closed-time path formulation of quantum field theory. There are also some new results for anomalies in the context of boundary value problems, and a new correction to the $a_5$ heat-kernel coefficient.