  We present a theoretical study of the $\gamma\gamma^{*} \to \pi^+\pi^-,
\pi^0\pi^0$ processes from the threshold through the $f_2(1270)$ region in the
$\pi\pi$ invariant mass. We adopt the Omn\`es representation in order to
account for rescattering effects in both s- and d-partial waves. For the
description of the $f_0(980)$ resonance, we implement a coupled-channel
unitarity. The constructed amplitudes serve as an essential framework to
interpret the current experimental two-photon fusion program at BESIII. They
also provide an important input for the dispersive analyses of the hadronic
light-by-light scattering contribution to the muon's anomalous magnetic moment.
