[eng] Photoproduction has been used at colliders for decades in order to study hadronic properties of matter. The energy and luminosity of recent and future colliders allow probing also the electroweak sector through photon-photon and photon-proton interactions. At the HERA electron-proton collider, studies of the W boson production provide a stringent test of the Standard Model. At the LHC, photoproduction has to be separated from the overwhelming background of partonic interactions. A powerful ‘tagging’ technique can be introduced by adding special detectors placed far from the interaction point to detect forward scattered protons, usually present in photon-mediated processes. The HECTOR software package was written in order to provide accurate simulation of forward protons trajectories in the LHC beam-lines. These tools have been used in order to study the photoproduction of top quarks via flavor-changing neutral currents. This process is practically absent in the Standard Model, while it appears in some of its extensions. Detection of such a process would thus be an evidence for the existence of physics beyond the Standard Model.