A bstract We present the most precise value for the Higgs boson cross-section in the gluon-fusion production mode at the LHC. Our result is based on a perturbative expansion through N 3 LO in QCD, in an effective theory where the top-quark is assumed to be infinitely heavy, while all other Standard Model quarks are massless. We combine this result with QCD corrections to the cross-section where all finite quark-mass effects are included exactly through NLO. In addition, electroweak corrections and the first corrections in the inverse mass of the top-quark are incorporated at three loops. We also investigate the effects of threshold resummation, both in the traditional QCD framework and following a SCET approach, which resums a class of π 2 contributions to all orders. We assess the uncertainty of the cross-section from missing higher-order corrections due to both perturbative QCD effects beyond N 3 LO and unknown mixed QCD-electroweak effects. In addition, we determine the sensitivity of the cross-section to the choice of parton distribution function (PDF) sets and to the parametric uncertainty in the strong coupling constant and quark masses. For a Higgs mass of m H = 125 GeV and an LHC center-of-mass energy of 13 TeV, our best prediction for the gluon fusion cross-section is σ = 48.58 p b − 3.27 p b + 2.22 p b theory ± 1.56 p b 3.20 % P D F + α s .