The observation of neutrinos produced in LHC collisions by the far-forward FASER and SND@LHC experiments in 2023 herald the new era of collider neutrino physics. These high-intensity forward neutrino fluxes from proton-proton LHC collisions enable novel opportunities in QCD, neutrino physics, BSM searches, and astroparticle physics. In this contribution, we briefly review the physics potential of neutrino deep-inelastic scattering (DIS) measurements at the LHC to shed light on proton and nuclear structure, both for ongoing far-forward experiments and for the proposed Forward Physics Facility (FPF) to operate concurrently with the HL-LHC. We consider the reach of LHC neutrino DIS to scrutinize the mechanisms of forward hadron production and constrain QCD in the ultra-small-𝑥 region. We also discuss how neutrino DIS measurements at these far-forward detectors enhance direct and indirect BSM searches at the HL-LHC.