Modern Quantum Electrodynamics (QED) has been extremely successful in describing the interactions of light
with matter as long as the perturbative approach remains valid. This is not true any longer when strong
electromagnetic fields are involved, such as those present in various astrophysical phenomena or expected
in a future lepton collider. Interesting new phenomena well beyond the linear response will then be observed.
In fact, at sufficiently high fields even the vacuum becomes nonlinear. Analogous to the atomic case, tunnel
ionization of the vacuum into electron-positron pairs can occur at field strengths comparable to the electron
mass in a Compton wavelength.
Although such fields are orders of magnitude away from what is possible with even the most intense lasers,
they can occur in the collisions of high energy electrons or photons with a strong laser field. In this talk,
I will review the conditions imposed by the presence of strong electromagnetic fields, describe the only
experiment that observed some of the relevant non-linear effects and provide an extensive outlook that highlights
the beginnings of a new exciting era in physics research.