Ultraperipheral collisions at the LHC and RHIC offer the highest currently available energy for photon-nucleon and photon-nucleus collisions. Thus they are a valuable tool for studying the gluonic structure of hadrons and nuclei at small x. We discuss recent theoretical work towards understanding such exclusive processes at NLO accuracy in QCD perturbation theory. These theoretical advances are also immediately relevant for understanding the physics of deep inelastic scattering at small x. We also discuss experimental results in ultraperipheral collisions, most prominently for exclusive vector meson production.