  An overwhelming number of theoretical predictions for hadron colliders
require parton distribution functions (PDFs), which are an important ingredient
of theory infrastructure for the next generation of high-energy experiments.
This whitepaper summarizes the status and future prospects for determination of
high-precision PDFs applicable in a wide range of energies and experiments, in
particular in precision tests of the Standard Model and in new physics searches
at the high-luminosity Large Hadron Collider and Electron-Ion Collider. We
discuss the envisioned advancements in experimental measurements, QCD theory,
global analysis methodology, and computing that are necessary to bring
unpolarized PDFs in the nucleon to the N2LO and N3LO accuracy in the QCD
coupling strength. Special attention is given to the new tasks that emerge in
the era of the precision PDF analysis, such as those focusing on the robust
control of systematic factors both in experimental measurements and theoretical
computations. Various synergies between experimental and theoretical studies of
the hadron structure are explored, including opportunities for studying PDFs
for nuclear and meson targets, PDFs with electroweak contributions or
dependence on the transverse momentum, for incisive comparisons between
phenomenological models for the PDFs and computations on discrete lattice, and
for cross-fertilization with machine learning/AI approaches. [Submitted to the
US Community Study on the Future of Particle Physics (Snowmass 2021).]
