  We perform a theoretical study based on dispersion relations of the reaction
\gamma\gamma\to \pi^0\pi^0 emphasizing the low energy region. We discuss how
the f_0(980) signal emerges in \gamma\gamma\to \pi\pi within the dispersive
approach and how this fixes to a large extent the phase of the isoscalar S-wave
\gamma\gamma\to \pi\pi amplitude above the K\bar{K} threshold. This allows us
to make sharper predictions for the cross section at lower energies and our
results could then be used to distinguish between different \pi\pi isoscalar
S-wave parameterizations with the advent of new precise data on
\gamma\gamma\to\pi^0\pi^0. We compare our dispersive approach with an updated
calculation employing Unitary Chiral Perturbation Theory (U\chiPT). We also pay
special attention to the role played by the \sigma resonance in
\gamma\gamma\to\pi\pi and calculate its coupling and width to gamma\gamma, for
which we obtain \Gamma(\sigma\to\gamma\gamma)=(1.68\pm 0.15) KeV.
