  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.
