Forward Physics with intact protons at the LHC

We will first describe how forward physics can lead to a better insight on the proton structure in terms of quarks and gluons at the LHC in the high gluon density regime. We will also discuss how detecting protons at the LHC leads to unprecedented sensitivities to Axion Like Particles and quartic photon anomalous coupling increasing the usual sensitivities to couplings by more than three orders of magnitude at the LHC.