We describe the beyond-standard model physics that can be performed at the LHC using intact protons in the final state. The gain on sensitivities to quartic $\gamma \gamma \gamma \gamma$, $\gamma \gamma WW$ and $\gamma \gamma \gamma Z$ anomalous couplings as examples and to the search for Axion-Like Particles is about two to three orders of magnitude with respect to standard methods at the LHC.