We argue that UPC at the LHC would allow to explore a wide range of the small x phenomena and would serve as a forerunner of program of experimental studies of small x dynamics to be performed within the small x program at the EIC. This includes elastic and incoherent diffractive J/ψ production off nuclei where one would be able to reach x=10-5; production of charm dijets both in the direct and resolved photon kinematics. Another promising process is production of leading J/ψ at large t with rapidity gap both in γp and γA scattering. This reaction would provide a unique opportunity to study propagation of a small color singlet dipole though a high density nuclear matter. Advantages of collecting information about neutron multiplicity in a zero-degree colorimeter are emphasized.