  In this document, we summarize the status and challenges of calculating
parton physics in lattice QCD for the US Particle Physics Community Planning
Exercise (a.k.a. "Snowmass"). While PDF-moments calculations have been very
successful and been continuously improved, new methods have been developed to
calculate distributions directly in $x$-space. Many recent lattice studies have
been focused on calculating isovector PDFs of the pion and nucleon, learning to
control systematics associated with excited-state contamination,
renormalization and continuum extrapolations, pion-mass and finite-volume
effects, etc. Although in some cases, the lattice results are already
competitive with experimental data, to reach the level of precision in a wide
range of $x$ for unpolarized nucleon PDFs impactful for future collider physics
remains a challenge, and may require exascale supercomputing power. The new
theoretical methods open the door for calculating other partonic observables
which will be the focus of the experimental program in nuclear physics,
including generalized parton distributions and transverse-momentum dependent
PDFs. A fruitful interplay between experimental data and lattice-QCD
calculations will usher in a new era for parton physics and hadron structure.
