  The unprecedented precision of experimental measurements at the Large Hadron
Collider (LHC) and the increased statistics that will be reached in the
High-Luminosity phase of the LHC (HL-LHC) are pushing the phenomenology
community to a new precision frontier, in which new challenges present
themselves and new questions arise. A key ingredients of theoretical
predictions at hadron colliders are the Parton Distribution Functions (PDFs) of
the proton. This contribution highlights some of the new developments in the
determination of PDFs from a global set of experimental data, from approximate
N3LO PDFs and the inclusion of theory uncertainties in PDF fits, to the
realisation of the non trivial interplay between parton densities at large-x
and possible signals of New Physics in high energy tails of the distributions,
which highlights the synergy between high energy and low energy experimental
programs.
