Fossil fuels provide a significant fraction of the global energy resources, and this is likely to remain so for several decades. Carbon dioxide (CO2) emissions have been correlated with climate change, and carbon capture is essential to enable the continuing use of fossil fuels while reducing the emissions of CO2 into the atmosphere thereby mitigating global climate changes. Among the proposed methods of CO2 capture, oxyfuel combustion technology provides a promising option, which is applicable to power generation systems. This technology is based on combustion with pure oxygen (O2) instead of air, resulting in flue gas that consists mainly of CO2 and water (H2O), that latter can be separated easily via condensation, while removing other contaminants leaving pure CO2 for storage. However, fuel combustion in pure O2 results in intolerably high combustion temperatures. In order to provide the dilution effect of the absent nitrogen (N2) and to moderate the furnace/combustor temperatures, part of the flue gas is recycled back into the combustion chamber. An efficient source of O2 is required to make oxy-combustion a competitive CO2 capture technology. Conventional O2 production utilizing the cryogenic distillation process is energetically expensive. Ceramic membranes made from mixed ion-electronic conducting oxides have received increasing attention because of their potential to mitigate the cost of O2 production, thus helping to promote these clean energy technologies. Some effort has also been expended in using these membranes to improve the performance of the O2 separation processes by combining air separation and high-temperature oxidation into a single chamber. This paper provides a review of the performance of combustors utilizing oxy-fuel combustion process, materials utilized in ion-transport membranes and the integration of such reactors in power cycles. The review is focused on carbon capture potential, developments of oxyfuel applications and O2 separation and combustion in membrane reactors. The recent developments in oxyfuel power cycles are discussed focusing on the main concepts of manipulating exergy flows within each cycle and the reported thermal efficiencies. Copyright © 2010 John Wiley & Sons, Ltd.