This paper reviews how numerical simulations of Quantum Chromodynamics (QCD) on a space-time lattice are now able to calculate many pieces of the internal structure of hadrons. The author focuses on results that are most useful for the planned Electron–Ion Collider (EIC). The review highlights advances for the pion, kaon and nucleon and explains how lattice QCD can provide complementary information to experiments.

Recent technical progress means some key quantities are now computed with percent-level precision. These include charges, form factors (which describe how the hadron’s internal charge or spin is distributed), and low-order Mellin moments (simple integrals of parton distribution functions, or PDFs, that measure how momentum is shared). New methods such as Large-Momentum Effective Theory (LaMET) let lattice calculations probe the full dependence of PDFs on the parton momentum fraction x by boosting hadrons on the lattice (typical boosts used so far are Pz ≈ 1.5–2 GeV). Calculations that use nonperturbative renormalization and perturbative matching up to next-to-next-to-leading order (NNLO) show consistency with phenomenological determinations in controlled kinematic regions.

State-of-the-art lattice simulations now use realistic setups: ensembles with two or three light quark flavors plus a heavier charm quark (noted as Nf=2+1 or Nf=2+1+1), pion masses at or near the physical value, lattice spacings as small as about a ≃ 0.05 fm, and spatial volumes L ≳ 6 fm. These choices allow controlled extrapolations to the physical continuum and infinite-volume limits. Still, further work is needed. Reaching higher hadron boosts (Pz ≳ 3 GeV), extending form factors to larger momentum transfer Q2, reducing discretization errors, and improving operator renormalization are all near-term goals. Simulations at the smallest lattice spacings are especially challenging because of long autocorrelation times.