  An investigation is performed of all non-leptonic kaon decays sensitive to
the chiral anomaly. Within the framework of chiral perturbation theory, there
are two classes of anomalous amplitudes at $O(p^4)$: reducible and direct
contributions. Only radiative transitions are affected by the anomaly. The
phenomenology of the decays $K_L \to \pi^+ \pi^- \gamma$ and $K^+ \to \pi^+
\pi^0 \gamma$ is studied in detail. Including the dominant contributions of
$O(p^6)$, the experimentally observed dependence of the direct emission
amplitude for $K_L \to \pi^+ \pi^- \gamma$ on the photon energy can be
understood. A survey is made of the rare ``anomalous'' decays $K \to \pi \pi
\gamma \gamma$ and $K \to 3 \pi \gamma (\gamma)$, including some numerical
estimates.
