In this talk, the authors focus on electromagnetic dilepton production from the QED-vacuum in relativistic heavy-ion collisions. Heavy ions in relativistic motion generate strong time-dependent EM fields with large Fourier components which give rise to sizable pair production. There are several motivations for this study: Lepton pair production by hadronic (Drell-Yan) processes has been widely discussed as a possible signature of the quark-gluon plasma formation. The dominant background will come from electromagnetic sources and could even mask the signals from the plasma phase. Electromagnetically produced lepton pairs also impose severe constraints on the design of relativistic heavy-ion colliders such as RHIC and LHC. In addition to the free pair production discussed above, pair-production with capture of the negatively charged lepton into a bound state is also possible. This change of the charge state of the ions is the leading mechanism for beam loss of relativistic colliders. Accurate predictions of the cross section for this process are important because the cross section increases with energy.