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Progress in the Determination of the Partonic Structure of the Proton

We review the current state of the art in the determination of the parton substructure of the nucleon, as expressed in terms of parton distribution functions (PDFs), and probed in high-energy lepton-hadron and hadron-hadron collisions, and we assess their implications for current precision collider phenomenology, in particular at the Large Hadron Collider (LHC). We review the theoretical foundations of PDF determination: the way cross sections are expressed in terms of PDFs using perturbative QCD factorization and evolution, the methodology used to extract PDFs from experimental data, and the way in which different physical processes can be used to constrain different PDFs. We summarize current knowledge of PDFs and the limitations in accuracy currently entailed for the computation of hadron collider processes, in particular at the LHC. We discuss the current main sources of theoretical and phenomenological uncertainties, and the direction of progress towards their reduction in the future.