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Cryogenic cooling of solid-state lasers has a number of important benefits, including the near vanishing of optical distortion in high average power lasers, as well as enhanced spectroscopic and lasing properties. These benefits are just beginning to be exploited to produce compact high average power lasers whose output is scalable, near diffraction limited, and whose efficiencies will exceed those of modern bulk solid-state lasers. In this paper, we review the history of cryogenically cooled solid-state lasers and the benefits of cryogenic cooling, including optical and laser properties and thermal and thermooptic properties; examine cryogenic amplifiers and cooling methods, including a straight-through propagation thin-disk configuration that does not perform well at room temperature, and summarize the experimental performance demonstrated to date. As a specific example, we examine the spectroscopic and lasing properties of Yb:YAG and show that compact high efficiency and high average power, near diffraction limited lasers (>100 kW) can be realized in the near future using presently available technology.