An X-ray Laser is a laser device which emits in the spectral region of X-rays, i.e., with wavelengths of only a few nanometers. In this extreme spectral region, traditional laser Gain media can not be used.
There are basically two different technical approaches:
The gain medium of a free Electron laser is an undulator, through which very high Energy electrons are sent.
Optical gain in the X-ray region can also be generated in plasmas, which themselves are typically created with laser beams or with electrical discharges. The laser transitions are between excited states of highly charged ions.
As it is difficult to construct a low-loss Laser Resonator for such short wavelengths, X-ray lasers are in most cases, particularly for shorter wavelengths, built without a Resonator and actually operate as ASE sources. This, however, decreases the spatial and temporal coherence.
Lasers can also be used in other ways for generating X-rays, in particular with high harmonic generation.