  We briefly summarize current experimental and theoretical results on the two
important processes of the low-energy hadron physics involving neutral pions,
the rare decay $\pi^0\to e^+e^-$ and the Dalitz decay of $\pi^0$, and provide a
new value for the ratio $R={\Gamma(\pi^0\to
e^+e^-\gamma(\gamma))}/{\Gamma(\pi^0\to\gamma\gamma)}=11.978(6)\times10^{-3}$,
which is by two orders of magnitude more precise than the current PDG average.
This value is obtained using the complete set of the next-to-leading-order
radiative corrections in the QED sector, and incorporates up-to-date values of
the $\pi^0$-transition-form-factor slope. The ratio $R$ translates into the
branching ratios of the two main $\pi^0$ decay modes:
$\mathcal{B}(\pi^0\to\gamma\gamma)=98.8131(6)\,\%$ and $\mathcal{B}(\pi^0\to
e^+e^-\gamma(\gamma))=1.1836(6)\,\%$. Furthermore, we present the complete set
of radiative corrections to the Dalitz decays
$\eta^{(\prime)}\to\ell^+\ell^-\gamma$ beyond the soft-photon approximation,
i.e. over the whole range of the Dalitz plot and with no restrictions on the
energy of a radiative photon. The corrections inevitably depend on the
$\eta^{(\prime)}\to\gamma^*\gamma^{(*)}$ transition form factors. For the
singly-virtual transition form factor appearing e.g. in the bremsstrahlung
correction, recent dispersive calculations are used. For the
one-photon-irreducible contribution at the one-loop level (for the
doubly-virtual form factor), we use a vector-meson-dominance-inspired model
while taking into account the $\eta$-$\eta^{\prime}$ mixing.
