We summarize recent work, where we calculated the cross sections for dilepton production by photon-photon processes in ultrarelativistic heavy-ion collisions from low (SPS) to high (LHC) energy.
We concentrate on very low pair transverse momenta, $P_T<0.15 \, \rm{GeV}$. Specifically, we investigate the interplay of thermal radiation with initial photon annihilation processes, $\gamma \gamma \to l^+ l^-$, triggered by the coherent electromagnetic fields of the incoming nuclei. For the thermal radiation, we employ the emission from the QGP and hadronic phases with in-medium vector spectral functions which describes the inclusive excess radiation observed over a wide range of collision energies.

We also discuss an approach to the impact-parameter dependent $P_T$-distribution of lepton pairs, which involves a Wigner transform of
the density matrix of Weizs\"acker--Williams photons.