  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.

High Energy Physics - Phenomenology;High Energy Physics - Experiment