Current status of the theory predictions for the Higgs inclusive cross section

The discovery of the Higgs boson opened the exploration of the sector that induces the breaking of the electroweak symmetry. The precise determination of the properties of the Higgs will serve as a fundamental probe of this sector. By the end of the Run I of the LHC, the largest limitation in this task was the uncertainty in the theoretical prediction of the Higgs production cross section. This limitation has been overcome through the calculation of the next-to-next-to-next to leading order (N^3LO) QCD contributions to the gluon-fusion channel. I will give an overview of the tools that were employed to achieve this result, discuss the contributions that enter the final cross section, and assess the remaining theory uncertainty.