The large equivalent-photon fluxes accompanying Pb ion beams at the LHC initiate photon-photon and photo-nuclear interactions which dominate when the colliding nuclei have large impact parameter (ultra-peripheral collisions). These electromagnetically-induced processes are sensitive to the nuclear wave-function and in particular the nuclear modifications of the nucleon parton distribution functions (nPDFs). As such, they are complementary to the ongoing p+A program at RHIC and the LHC, as well as the upcoming electron-ion collider (EIC) program in the US. High-mass dilepton pair continuum rates have been measured and compared with theoretical predictions to test expectations for two-photon interactions, and good agreement with model calculations is obtained. Evidence for the elastic scattering of photons $\gamma\gamma\to\gamma\gamma$ (``light-by-light'' scattering) will be presented, a previously unobserved process made possible by the high photon flux and low event pileup provided by the LHC. While of intrinsic interest as a heretofore-unobserved standard model process, it has also been proposed as a clean channel for searches for beyond the standard model (BSM) physics.