Abstract: "At the dawn of Run II, LHC data analysis and interpretation requires more than ever high-precision theoretical calculations, of which a crucial component are the Parton Distribution Functions (PDFs) of the proton. PDFs determine how the proton energy is distributed among quarks and gluons. Uncertainties in Parton Distributions dramatically limit the scientific output of essential LHC analyses, such as the extraction of the Higgs boson properties, where deviations from the tight Standard Model predictions represent a smoking gun for New Physics; or the search for BSM high-mass resonances, where PDF uncertainties are so large that, even in the case of discovery, the characterization of the underlying New Physics scenario would be extremely challenging. In this talk I will introduce a novel approach to PDF determination, based on Artificial Neural Networks and Machine Learning. I will then illustrate the relevance of precision PDF analyses for LHC phenomenology, including Higgs boson characterization, PDFs with all-order perturbative resummations, and the constraints on PDFs from ATLAS, CMS and LHCb measurements. I will conclude by highlighting a remarkable connection between forward D meson production at LHCb, the small-x gluon PDF, and the the calculation of the prompt neutrino flux at neutrino telescopes."