  Ultra-peripheral collisions are the energy frontier for photon-mediated
interactions, reaching, at the Large Hadron Collider (LHC), $\gamma-p$ center
of mass energies five to ten times higher than at HERA and reaching
$\gamma\gamma$ 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 $3\times10^{-6}$, 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 $Q^2$. High-statistics $\rho^0$ data probe the spatial
distribution of the interaction sites; the site distribution is given by the
Fourier transform of $d\sigma/dt$.
  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).
