Parton Distribution Functions and Their Impact on Precision of the Current Theory Calculations

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.