  We summarize recent work in determining the transition form factor (TFF) of
the neutral pion ($\pi^0 \to \gamma^*\gamma^*$), by solving the
non-perturbative Dyson-Schwinger and Bethe-Salpeter equations. We first study
the transition form factor, followed by the rare decay $\pi^0 \to e^+ e^- $,
which requires the TFF as input. In addition to the aspects of truncation
required to compute the solution, we discuss unexpected behavior in the large
$Q^2$ regime (with $Q^2$ the photon virtuality), and also touch on a path
deformation in the complex plane to access the total decay rate for the rare
decay.
