Cryogenic X-ray spectrometers are advantageous in the spectrum research for weak and diffusive X-ray source due to their high energy resolution, high detection efficiency, low noise level and non-dead-layer properties. Their energy resolution independent of the incident X-ray direction also makes them competitive in diffusion source detection. The requirements for X-ray spectrometers have heightened in recent years with the rapid development of large scientific facilities where X-ray detection is demanded, including beamline endstations in synchrotron and X-ray free electron laser facilities, accelerators, highly charged ion traps, X-ray space satellites, etc. Because of their excellent performances, cryogenic X-ray detectors are introduced into these facilities, typical examples of which are APS, NSLS, LCLS-II, Spring-8, SSNL, ATHENA, HUBS. In this paper, we review the cryogenic X-ray spectrometers, from the working principle and classification, system structure, major performance characteristics to the research status and trend in large scientific facilities in the world.