The paper presents a new set of parton distributions (PDFs), NNPDF3.1, which updates the previous set, NNPDF3.0. The update is motivated by recent progress in methodology and available data. Methodologically, the new set parametrizes and determines the charm PDF alongside the light-quark and gluon PDFs, increasing the number of independent PDFs from seven to eight. Thematically, the new set includes recent experimental data from the D0 electron and muon W asymmetries, complete LHCb measurements of W and Z production at 7 and 8 TeV, and new ATLAS and CMS measurements of inclusive jet and electroweak boson production. Additionally, it includes top-quark pair differential distributions and the transverse momentum of Z bosons from ATLAS and CMS for the first time. The impact of parametrizing charm is investigated, showing improved accuracy and stability of the PDFs. The new data are studied by producing PDF sets based on reduced datasets, revealing significant improvements in both uncertainties and agreement with the previous set at the one-sigma level. The most notable changes are in the light-quark flavor separation and the determination of the gluon. The implications of NNPDF3.1 for LHC phenomenology at Run II, comparisons with recent LHC measurements at 13 TeV, and updated predictions for Higgs production cross-sections are discussed. The strangeness and charm content of the proton are also explored in light of the improved dataset and methodology. The NNPDF3.1 PDFs are delivered in both Hessian and optimized Monte Carlo sets, with a reduced number of replicas.The paper presents a new set of parton distributions (PDFs), NNPDF3.1, which updates the previous set, NNPDF3.0. The update is motivated by recent progress in methodology and available data. Methodologically, the new set parametrizes and determines the charm PDF alongside the light-quark and gluon PDFs, increasing the number of independent PDFs from seven to eight. Thematically, the new set includes recent experimental data from the D0 electron and muon W asymmetries, complete LHCb measurements of W and Z production at 7 and 8 TeV, and new ATLAS and CMS measurements of inclusive jet and electroweak boson production. Additionally, it includes top-quark pair differential distributions and the transverse momentum of Z bosons from ATLAS and CMS for the first time. The impact of parametrizing charm is investigated, showing improved accuracy and stability of the PDFs. The new data are studied by producing PDF sets based on reduced datasets, revealing significant improvements in both uncertainties and agreement with the previous set at the one-sigma level. The most notable changes are in the light-quark flavor separation and the determination of the gluon. The implications of NNPDF3.1 for LHC phenomenology at Run II, comparisons with recent LHC measurements at 13 TeV, and updated predictions for Higgs production cross-sections are discussed. The strangeness and charm content of the proton are also explored in light of the improved dataset and methodology. The NNPDF3.1 PDFs are delivered in both Hessian and optimized Monte Carlo sets, with a reduced number of replicas.