This article reviews the progress in the development of practical table-top sources of soft x-ray laser radiation. The field is rapidly approaching the stage at which soft x-ray lasers sufficiently compact to fit onto a normal optical table will be routinely utilized in science and technology. This is the result of recent advances in the amplification of soft x-ray radiation in both compact laser-pumped and discharge-pumped devices. The use of excitation mechanisms that take full advantage of new ultrafast high power optical laser drivers and multiple pulse excitation schemes has resulted in the demonstration of saturated soft x-ray amplification at wavelengths as short as 14 nm using several Joule of laser-pump energy. Moreover, several schemes have demonstrated significant gain with only a fraction of a Joule of laser-pump energy. In addition, the demonstration of saturated table-top soft x-ray lasers pumped by very compact capillary discharges has shattered the notion that discharge-created plasmas are insufficiently uniform to allow for soft x-ray amplification, opening a route for the development of efficient, high average power soft x-ray lasers. Recently, a table-top capillary discharge laser operating at 46.9 nm has produced millijoule-level laser pulses at a repetition rate of several Hz, with a corresponding spatially coherent average power per unit bandwidth comparable to that of a beam line at a third generation synchrotron facility. This review summarizes fundamental and technical aspects of table-top soft x-ray lasers based on the generation of population inversions in plasmas, and discusses the present status of development of specific laser systems.