Towards next-gen parton distribution and fragmentation functions

The interest into parton distribution functions (PDFs) and fragmentation functions (FFs) in current high energy physics research is twofold. On the one hand, they are fundamental objects to conduct precision phenomenology studies, e.g. at the Large Hadron Collider (LHC), to determine the Standard Model parameters and search for new physics. On the other hand, they are also a means to understand the inner structure and dynamics of hadrons, e.g. in regards to the proton spin decomposition at the future Electron Ion Collider (EIC). This thesis presents advancements in PDF and FF determinations contributing to upcoming releases by the NNPDF collaboration. For PDFs, three topics are addressed: (i) assessing the K-factor approximation versus exact NNLO calculations; (ii) evaluating the compatibility of new data with existing PDFs, accounting for all relevant theoretical and experimental uncertainties; and (iii) studying the impact of new data, with focus on processes sensitive to the gluon PDF: single-inclusive jet and di-jet production in proton-proton collisions and deep-inelastic scattering, and top-quark pair production in proton-proton collisions. For FFs, I extend the NNPDF framework through: (i) implementation of time-like evolution in EKO; (ii) extension of PineAPPL to handle multiple convolutions of PDFs and FFs, including the corresponding factorization scales and the polarization of the initial and final states; and (iii) development of a new code, vhf, for computing SIA and SIDIS cross sections. All of these developments are crucial to prepare the release of next-gen PDF and FF sets that will allow us to take advantage of the forthcoming LHC and EIC physics programs as much as possible.