Ultrarelativistic heavy ions are accompanied by a large flux of quasi-real Weizs\"acker-Williams photons.
This opens a broad range of research possibilities, as the Weizs\"acker-Williams photons can be used to study photon-photon fusion reactions as well as photonuclear reactions in a wide range of energies.

Of special interest here are diffractive photoproduction reactions, which appear in two major classes: the coherent diffraction in which the target nucleus stays intact and the incoherent (or quasielastic) diffraction in which the nucleus breaks up, but no additional particles are produced in the nuclear fragmentation region.

We will discuss the coherent diffractive photoproduction of heavy vector mesons $J/\psi$. Good agreement with available experimental data by the ALICE and LHCb collaborations can be obtained within a color-dipole approach. Here additional nuclear shadowing from the $c \bar c g$-Fock state is needed to obtain agreement with data.

Very recently, the role of Weizs\"acker-Williams photons in peripheral, inelastic, heavy ion collisions has come under scrutiny.
Recent measurements of dilepton production of the STAR collaboration in $\sqrt{s_{NN}}$=200\,GeV Au-Au collisions indicate an excess at small pair $p_T$ most notably in peripheral collisions. We show, that it can be that has attributed to the initial photon fusion which is most significant at small pair transverse momenta. The centrality dependence of the pair transverse momentum distribution is calculated in a novel factorization approach involving Wigner distributions of photons.