Constraints on parton distributions and the strong coupling from LHC jet data

Jet production at hadron colliders provides powerful constraints on the parton distribution functions (PDFs) of the proton, in particular on the gluon PDF. Jet production can also be used to extract the QCD coupling constant and to test its running with the momentum transfer up to the TeV region. In this review, I summarize the information on PDFs and the strong coupling that has been provided by Run I LHC jet data. First of all, I discuss why jet production is directly sensitive to the gluon and quark PDFs at large-x, and then review the state-of-the-art perturbative calculations for jet production at hadron colliders and the corresponding fast calculations required for PDF fitting. Then I present the results of various recent studies on the impact on PDFs, in particular the gluon, that have been performed using as input jet measurements from ATLAS and CMS. I also review the available determinations of the strong coupling constant based on ATLAS and CMS jet data, with emphasis on the fact that LHC jet data provides, for the first time, a direct test of the $\alpha_s(Q)$ running at the TeV scale. I conclude with a brief outlook on possible future developments.