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In this review we concentrate our attention on X-ray laser research and development covering the so called soft X-ray region (down to ~ 10 nm) and the ``water window'' region (down to 2.3 – 4.4 nm). We present the development of soft X-ray lasers (SXLs) and their applications using primarily collisional and recombination schemes. We present the paths towards compact systems and major achievements to date. We discuss conditions for using both schemes to reach the ``water window'' region. In this discussion we also present another possible schemes based on photo-pumping, inner shell transitions in atoms and ions and ``Doppler Compression'' of IR laser radiation down to the X-ray region with its intrinsic tunability possibility. A significant part of the review is dedicated to the wide range of applications of SXLs with wavelengths at and above 10 nm. Also discussed is the potential of extending the range of biological applications for the ``water window'' region.

We report the results of a soft-X-ray laser experiment in which five Nd-laser beams are used for producing a 6-cm long aluminium plasma column. Population inversion occurs for the 3d-5f transition of lithiumlike ions (λ = 105.7 A) according to the plasma recombination scheme. A double-pass device is achieved with a W/C multilayer mirror. Double-pass is shown to increase largely the intensity and the directivity of the beam at 105.7 A. A plasma produced from thin aluminium target supplies a gain coefficient of 0.5 cm-1, whereas population inversion is strongly reduced by radiation trapping in the case of massive targets.

This paper reports time-resolved measurements of gain at 105.7 A in an aluminum plasma produced by a laser. It is shown that the amplification occurs during the plasma cooling, at the end of the laser pulse. The observed time-variation of the gain agrees with the prediction of a plasma recombination model used for calculating the level populations of the lithium-like Al10+ ions.