This thesis is dedicated to the construction and applications of Parton Distribution Functions (PDFs), which are precise enough that are suitable for comparison with high-precision collider data from the LHC. We first review the theoretical framework and explain how PDFs should be used in practice, presenting tools that allow to seemingly convert between different representations of PDF uncertainties. We then discuss how these tools are used to construct the PDF4LHC15 combined sets, which implement the recommendation of the PDF4LHC group, and provide detailed benchmarks of each of the combined sets. We describe NNPDF 3.1, the first global PDF analysis to provide percent level uncertainties for many relevant observables while being validated by a closure test, with particular emphasis to the issues that appeared during its preparation and the resources used solve them. Finally we present a determination of the strong coupling constant based on the global NNPDF3.1 fit. We use a new methodology that correctly propagates all the uncertainties from the PDFs to the result.