  We perform a detailed study of double Higgs production via gluon fusion in
the Effective Field Theory (EFT) framework where effects from new physics are
parametrized by local operators. Our analysis provides a perspective broader
than the one followed in most of the previous analyses, where this process was
merely considered as a way to extract the Higgs trilinear coupling. We focus on
the $hh \to b\bar b\gamma\gamma$ channel and perform a thorough simulation of
signal and background at the 14 TeV LHC and a future 100 TeV proton-proton
collider. We make use of invariant mass distributions to enhance the
sensitivity on the EFT coefficients and give a first assessment of the impact
of jet substructure techniques on the results. The range of validity of the EFT
description is estimated, as required to consistently exploit the high-energy
range of distributions, pointing out the potential relevance of dimension-8
operators. Our analysis contains a few important improvements over previous
studies and identifies some inaccuracies there appearing in connection with the
estimate of signal and background rates. The estimated precision on the Higgs
trilinear coupling that follows from our results is less optimistic than
previously claimed in the literature. We find that a ~30% accuracy can be
reached on the trilinear coupling at a future 100 TeV collider with 3 ab^-1.
Only an O(1) determination seems instead possible at the LHC with the same
amount of integrated luminosity.
