The closed Brayton cycle (CBC) has become a promising solution for the high-energy density power conversion unit in underwater and space applications. Differing from the design requirements of the grounded plant, the CBC in the underwater application gives priority to the compact size. Therefore, there is a need to provide a summary of the current research, particularly on working fluid and turbomachinery, with the view to obtaining the strategies adopted in power conversion unit to meet the design requirements of the underwater and space application. This paper presented the comprehensive considerations behind the selection of helium as the ideal working fluids for underwater and space applications and reviews the various predictions methods of the un-acquainted physical properties of noble gas, among which the method pertaining to the Chapman-Enskog kinetic theory and the law of the corresponding state is more precise with the comprehensive accuracies of 2% for pure gas and 5% for the binary mixture. The studies on the characteristics of noble gas to support the application feasibility of the existing aerodynamic method to it were also reviewed. Two strategies to reduce the size of the power conversion unit, based on highly-loaded design and He-Xe turbomachinery design, were presented. Through the strategies, the stage number of the compressor under the given pressure ratio can reduce by about 75% compared with the prototype. Moreover, the paper also paid an attention to the similarity modeling method in the performance map of turbomachinery between the noble gas and air. Based on the review, the current problems encountered and the expected future breakthroughs were highlighted.