  This work aims to review several aspects of the current status of the rare
$\pi^0\to e^+e^-$ decay. A particular emphasis is made on radiative corrections
and detailed interpretation of related quantities, some numbers appearing in
the literature are updated, and the connection with the Dalitz decay, $\pi^0\to
e^+e^-\gamma$, is discussed. This comes timely as it is aligned with an
announcement of a preliminary result of a new branching-ratio measurement done
by the NA62 Collaboration, which brings new light into an earlier-reported
discrepancy between the Standard Model prediction and the
(until-recently-latest) precise KTeV result.
