Semiconductor-based devices in various fields such as night vision, space exploration, medical inspection, telecommunication, among others could benefit from operating at cryogenic temperatures. Besides, cryogenic temperatures also can offer some unique capabilities to superconducting devices, which are not available at ambient temperature. However, existing cryocoolers are oversized in terms of size and cooling power. Widespread use of these electronic devices requires cryocoolers that are small, low cost, low interference, and reliable. This review presents an overview of cooling cycles and discusses the opportunities and difficulties when adopting these cycles for realizing cryogenic temperatures above 1 K in microscale. It is found by comparison that, at present, fluid-based cryocoolers are more suitable for miniaturization. Concerning the miniaturization of fluid-based cryocoolers, emphasis is put on the effect that scaling has on the gross and net cooling power and on various parasitic losses, the microscale manufacturing technologies, and the state of the art of microcoolers. Some aspects that remain to be further developed for widespread use of cryogenic microcooling, are considered at the end of this review.