Parton distribution functions and theory parameters: an NNPDF perspective

Parton Distribution Functions (PDFs) are a key ingredient in theoretical predictions for Large Hadron Collider (LHC) observables and play a central role in the extraction of precision Standard Model (SM) and Beyond the SM (BSM) parameters from LHC data. Recent analyses demonstrate that the determination of fundamental SM parameters such as $\alpha_s(m_Z)$, $m_W$, $m_t$, and $\sin^2\theta_W$ is strongly influenced by the choice of input PDFs. In this contribution, we present the status and challenges of PDF determination from the NNPDF perspective, both in stand-alone fits and in joint extractions with (B)SM parameters. We place particular emphasis on results for $\alpha_s(m_Z)$, $m_t$, and Wilson coefficients in the SM Effective Field Theory (SMEFT) framework.