Ultra-peripheral collisions are the energy frontier for photon-mediated interactions, reaching, at the Large Hadron Collider (LHC), γ−p center of mass energies five to ten times higher than at HERA and reaching γγ energies higher than at LEP. Photoproduction of heavy quarkonium and dijets in pp and pA collisions probes the gluon distribution in protons at Bjorken-x values down to 3×10−6, far smaller than can be otherwise studied. In AA collisions, these reactions probe the gluon distributions in heavy ions, down to x values of a few 10−5. Although more theoretical work is needed to nail down all of the uncertainties, inclusion of these data in current parton distribution function fits would greatly improve the accuracy of the gluon distributions at low Bjorken-x and low/moderate Q2. High-statistics ρ0 data probe the spatial distribution of the interaction sites; the site distribution is given by the Fourier transform of dσ/dt. After introducing UPCs, this review presents recent measurements of dilepton production and light-by-light scattering and recent data on proton and heavy nuclei structure, emphasizing results presented at Quark Matter 2017 (QM2017).