Protons and neutrons are known to be the building blocks of matter, and also known to be the bound states of quarks and gluons - the partons, whose dynamics is best described by Quantum Chromodynamics (QCD). Perturbative QCD has been very successful in interpreting and predicting high-energy hadronic scattering processes by factorizing the leading contribution to the physical cross sections into a convolution of the perturbatively calculable short-distance part and the universal long-distance parton distribution functions (PDFs) of colliding hadrons. Besides testing QCD dynamics at the short-distance, these cross sections also probe partonic structure inside a colliding hadron via PDFs, which are often interpreted as the probability densities of finding a parton inside a hadron with a given longitudinal momentum fraction.

In this thesis I discuss the possibilities to explore the rich partonic dynamics inside a hadron or a large nucleus beyond the probability distributions. I will first explain why a difference of two transverse-spin dependent cross sections (or the measurement of the single transverse-spin asymmetry) can directly probe a set of new three-parton correlation functions. These correlation functions provide the first direct information on quantum correlation between quarks and gluons inside a polarized hadron. I will describe the basic formalism and the experimental measurements of these correlation functions. I will present the first derivation of evolution equations (or renormalization group equations) for these correlation functions. I will then discuss how to use the nuclear dependence of high energy nuclear collisions to extract the information on four-parton correlations inside a large nucleus or a nuclear medium. The measurements of the spin asymmetry and the anomalous nuclear dependence provide us new opportunities to explore the QCD dynamics and hadron structure beyond the parton probability distributions.