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The Large Hadron Collider has a broad physics program devoted to the studies of known particles and interactions as well as searching for phenomena yet unknown. In recent years, one of the interesting outcomes from the LHC experiments were the measurements of collisions of photons, which originate from the electromagnetic fields of the particles accelerated by the LHC. I will discuss the physics of these processes, the motivation to study them, and the experimental methods exploited in the measurements. I will particularly focus on a recent method using dedicated detectors that can register protons from which the interacting photons were emitted.