A review of forward proton tagging at 420m at the LHC, and relevant results from the Tevatron and HERA

We review the theoretical and experimental motivations behind recent proposals to add forward proton tagging detectors to the LHC experiments as a means to search for new physics. We also review the current diffractive programs at the Tevatron and HERA, focusing in particular on measurements which will have a direct impact on the case for forward detectors at the LHC.