Printed circuit heat exchangers (PCHEs) are a promising technology for helium and supercritical CO2 Brayton cycles due to their highly compact construction, very high heat transfer coefficients, capability to withstand high pressures and wide range of operating temperatures. The purpose of this review is to provide a comprehensive understanding of the performance of PCHEs based on available literature and survey of heat exchangers currently available on the market. First, the fundamental principles, including material selection, manufacturing and assembly, are introduced. Then, PCHEs with different flow passages are summarized and analysed along with their heat transfer and pressure drop characteristics. Next, geometric design optimisation of PCHEs is summarised and discussed, taking into consideration the complex relationships between heat transfer enhancement and pressure drop penalty, compactness and fluid inventory as well as capital cost. Finally, knowledge gaps are identified and suggestions for further research to address these for a wider range of applications are presented. The review covers relatively new heat exchangers on the market as well as designs that are still under development. Although extensive work has already been done in this field, and PCHEs are well established in the petrochemical industry, significantly more work is needed to increase their attractiveness for a wider range of applications. This work should be aimed at the optimisation of flow passage configurations in terms of thermohydraulic performance, complexity and manufacturing costs, development and selection of materials to increase further the range of high temperature and pressure operation, and the development of more generalised correlations for performance prediction and overall design optimisation.