Full NLO QCD corrections to Higgs-pair production in the Standard Model and beyond

Higgs-pair production is one of the targets of the high-luminosity LHC and of future hadron colliders, as it allows for a direct probe of the trilinear Higgs coupling and hence of the mechanism behind electroweak symmetry breaking. This contribution focuses on the impact of the full next-to-leading order QCD corrections to Higgs-pair production via gluon fusion, the main production mechanism at hadron colliders, in the Standard Model and in Two-Higgs-Doublet models. The uncertainties due to the top-mass scale-and-scheme choice will be discussed.