  X-ray free electron lasers will be constructed in this decade, both at SLAC
in the form of the so-called Linac Coherent Light Source as well as at DESY,
where the so-called TESLA XFEL laboratory uses techniques developed for the
design of the TeV energy superconducting electron-positron linear accelerator
TESLA. Such X-ray lasers may allow also for high-field science applications by
exploiting the possibility to focus their beams to a spot with a small radius,
hopefully in the range of the laser wavelength. Along this route one obtains
very large electric fields, much larger than those obtainable with any optical
laser of the same power. We consider here the possibility of obtaining an
electric field so high that electron-positron pairs are spontaneously produced
in vacuum (Schwinger pair production) and review the prospects to verify this
non-perturbative production mechanism for the first time in the laboratory.
