Due to its large reserves, coal is expected to continue to play an important role in the future. However, specific and absolute CO2 emissions are among the highest when burning coal for power generation. Therefore, the capture of CO2 from power plants may contribute significantly in reducing global CO2 emissions. This review deals with the oxyfuel process, where pure oxygen is used for burning coal, resulting in a flue gas with high CO2 concentrations. After further conditioning, the highly concentrated CO2 is compressed and transported in the liquid state to, for example, geological storages. The enormous oxygen demand is generated in an air-separation unit by a cryogenic process, which is the only available state-of-the-art technology. The generation of oxygen and the purification and liquefaction of the CO2-enriched flue gas consumes significant auxiliary power. Therefore, the overall net efficiency is expected to be lowered by 8 to 12 percentage points, corresponding to a 21 to 36% increase in fuel consumption. Oxygen combustion is associated with higher temperatures compared with conventional air combustion. Both the fuel properties as well as limitations of steam and metal temperatures of the various heat exchanger sections of the steam generator require a moderation of the temperatures during combustion and in the subsequent heat-transfer sections. This is done by means of flue gas recirculation. The interdependencies among fuel properties, the amount and the temperature of the recycled flue gas, and the resulting oxygen concentration in the combustion atmosphere are investigated. Expected effects of the modified flue gas composition in comparison with the air-fired case are studied theoretically and experimentally. The different atmosphere resulting from oxygen-fired combustion gives rise to various questions related to firing, in particular, with regard to the combustion mechanism, pollutant reduction, the risk of corrosion, and the properties of the fly ash or the deposits that form. In particular, detailed nitrogen and sulphur chemistry was investigated by combustion tests in a laboratory-scale facility. Oxidant staging, in order to reduce NO formation, turned out to work with similar effectiveness as for conventional air combustion. With regard to sulphur, a considerable increase in the SO2 concentration was found, as expected. However, the H2S concentration in the combustion atmosphere increased as well. Further results were achieved with a pilot-scale test facility, where acid dew points were measured and deposition probes were exposed to the combustion environment. Besides CO2 and water vapour, the flue gas contains impurities like sulphur species, nitrogen oxides, argon, nitrogen, and oxygen. The CO2 liquefaction is strongly affected by these impurities in terms of the auxiliary power requirement and the CO2 capture rate. Furthermore, the impurity of the liquefied CO2 is affected as well. Since the requirements on the liquid CO2 with regard to geological storage or enhanced oil recovery are currently undefined, the effects of possible flue gas treatment and the design of the liquefaction plant are studied over a wide range.