Higgs and Beyond the Standard Model physics with the FP420 detector at the LHC

The physics case of the FP420 R&D project aiming at the installation of proton detectors in the LHC tunnel at 420 m from the ATLAS and CMS interaction points, is presented. The motivations of the measurements accessible with FP420 -- exclusive Higgs production (pp --> p H p) and photon-induced processes (pp --> p gamma p --> p X p, pp --> p gamma gamma p --> p X p, where X is sensitive to new physics) -- are outlined.