Parton distribution and correlation functions describe the relation between a hadron and the quarks and gluons (or partons) within it, and carry rich information on hadron’s partonic structure. They cannot be calculated by QCD perturbation theory, and have been extracted from experimental data of high energy scattering cross sections with the aid of QCD factorization. Parton distribution functions are the simplest of all correlation functions. Without them, we would not be able to understand the hard probes in hadronic collisions, including the Higgs discovery at the LHC. In this talk, I will discuss how can the QCD factorization help extract the same parton distribution and correlation functions from various “lattice cross sections” – hadron matrix elements that can be systematically calculated by using lattice QCD techniques. With the ab initio lattice QCD calculations, complementary to the experimental measurements, I argue that we are entering a new era of exploring hadron’s internal structure in terms of the dynamics of quarks and gluons.