Whereas most LHC physics is concerned with very rare or exotic processes such as the production of Higgs bosons or new particles beyond the Standard Model, our understanding of what 'usually' happens in high energy proton-proton collisions is surprisingly poor. This talk will review LHC measurements of some of the most commonly occurring processes, which lead to final states with intact protons. These will include elastic scattering (pp->pp), diffractive dissociation central exclusive production (pp->pXp). The talk will also cover prospects for future studies with unprecedented high luminosities.