Anomalous gauge interactions in photon collisions at the LHC and the FCC

The forward proton detectors recently installed and operating at the LHC open the possibility to observe photon collisions with high precision, providing a novel window on physics beyond the Standard Model. We review recent simulations and theoretical developments about the measurement of anomalous ${\gamma}{\gamma}{\gamma}{\gamma}$ and $Z{\gamma}{\gamma}{\gamma}$ interactions. The searches for these anomalous gauge interactions are expected to set bounds on a wide range of particles including generic electroweak particles, neutral particles with dimension-5 coupling to gauge bosons, polarizable dark particles, and are typically complementary from new physics searches in other channels.