•Closed-cycle gas turbine applicable to a wide range of heat sources.•Working fluids include air, nitrogen, supercritical CO2 and helium.•Review of important R&D programmes and operated plants.•Heat exchangers are significant driver in the capital cost and technical viability.•Demonstration plant essential before commercial deployment. In the last few years, there has been considerable interest in closed-cycle gas turbine power plants due to the important contribution it can make to meeting worldwide energy demands. Closed-cycle gas turbine has the potential to serve as power conversion system for a wide range of energy sources such as fossil fuel, concentrated solar power, nuclear, biomass and waste heat. However, there is a need to provide an update on the development of closed-cycle gas turbine with a view to identifying the challenges and the opportunities for future commercialisation. This paper is a review of the research activities and studies carried out worldwide so far on closed-cycle gas turbine. The historical development in chronological order was presented first, followed by a review of some fundamental features such as heat sources, working fluids, heat exchangers and cycle layouts/configurations. Important research programmes and experimental/pilot plants as well as previous commercially operated plants were also reviewed. Moreover, various studies based on modelling and simulation of closed-cycle gas turbine were reviewed, in addition to the operation and control strategies. Based on the review studies, the challenges ahead and potential future breakthroughs were highlighted in different aspects such as heat source technologies, power conversion system and demonstration plant.