Photon-induced reactions in ultra-peripheral collisions (UPCs) of heavy nuclei at the LHC have been studied using the ALICE detector for several years. The ALICE detector can measure the photoproduction cross section for vector mesons at various rapidities, centre-of-mass energies and collision systems. In addition to the recent ALICE studies of the rapidity and momentum transfer dependence of coherent $\rm{J/\psi}$ photoproduction, new results on incoherent $\rm{J/\psi}$ photoproduction will be discussed. These results complement coherent $\rm{J/\psi}$ measurements and provide additional sensitivity to probing nuclear gluon effects.