The physics of soft x rays is closely tied to fundamental investigations in solid state physics, materials science, plasma physics, astrophysics, and biology. Recent progress in the technology of x-ray sources and optical elements for x rays raises the issue of the wide use of soft x rays in technology (x-ray lithography) and in laboratory and commercial microanalysis. This article gives a review of the present state of undulator and laser sources of soft x rays. In undulators the radiation is emitted by electrons in a spatially periodic magnetic field, and in lasers it is emitted by a plasma formed by focusing a powerful visible or infrared laser on a solid surface. Particular attention is paid in this article to the conceptual possibilities and the results that have been published in the last three years; that is, since publication of the review by D. Attwood, K. Halbach, and Kwang-Je Kim [Science 228, 1265 (1985)], which also appears in the present issue of Uspekhi Fizicheskikh Nauk. The highest pulsed brightness attained to date has been from x-ray lasers. However, for many problems the most important factor is the time average of the brightness (or flux density). For these problems the undulator is the preferred source. Moreover, undulators afford the possibility of tuning over the spectrum and covering a wider range of wavelength.