  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
scrutinise 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.
