Strong electromagnetic fields of accelerated heavy ions at the LHC can be used to probe photon-photon and photon-hadron interactions in a new kinematic regime. ALICE has extensively studied these processes in ultra-peripheral collisions (UPC) characterized by impact parameters larger than the sum of nuclear radii. In recent years, photon-induced processes have been also observed in heavy ion collisions with nuclear overlap.
In this contribution, we review recent ALICE results on the coherent $J/\psi$ photoproduction in Pb-Pb UPCs probing nuclear gluon distributions at low Bjorken-x, and the first measurement at the LHC of the dissociative $J/\psi$ photoproduction off protons sensitive to quantum fluctuations of the proton structure. Latest ALICE measurements on the coherent $J/\psi$ photoproduction in collisions with nuclear overlap will be also presented. Finally, the prospects for future measurements of photon-induced processes in the LHC Run 3 and 4 will be discussed.