Physics with TeV neutrinos at the LHC and beyond

Proton-proton collisions at the LHC produce an immense flux 
of high-energy (up to several TeV) neutrinos along the beam (forward) 
direction. The breakthrough observation of LHC neutrinos by FASER and 
SND@LHC in March 2023, followed by the first neutrino cross-section 
measurements at the TeV scale and the first data-driven constraints on 
the LHC neutrino fluxes in 2024, open many exciting opportunities in 
particle physics. In this talk I present the unprecedented reach of 
current (FASER, SND@LHC) and future (FASER2, AdvSND, FLArE) forward LHC 
neutrino experiments for studies of SM and BSM physics, focusing on 
their impact for QCD and neutrino physics. I demonstrate that these 
experiments effectively extend the CERN infrastructure with an 
Neutrino-Ion Collider, enabling novel opportunities to pin down hadronic 
structure, opening a window to the gluon content  of the proton in 
regions outside the coverage of any other experiment, and providing the 
first laboratory-based validation of cross-sections relevant for 
high-energy astroparticle studies. I also discuss the current status of 
Monte Carlo event generators for high-energy neutrino DIS. Finally, if 
time allows, I will present the physics potential of a FASER-like 
detector operating in the context of a 100 TeV proton collider such as 
the FCC-hh.