The precise measurement of the properties of the Higgs boson is a crucial part of the physics program at the Large Hadron Collider (LHC). In addition to the total Higgs production cross section, kinematic distributions such as the Higgs transverse momentum are of particular interest due to its sensitivity to modifications of Higgs Yukawa couplings, and therefore to physics beyond the Standard Model. In this talk I review the pT resummation for Higgs boson production in hadron colliders as formulated by Soft Collinear Effective theory. I will present predictions for the Higgs pT spectrum in the gluon fusion channel at N3LL' resummation order and matched to N3LO fixed order, including fiducial cuts employed at the LHC. Exploiting the aforementioned calculation, I present the first prediction for its total cross section with fiducial cuts at N3LO, and further improved by resummation.