Oxyfuel combustion with carbon capture and sequestration (CCS) is a carbon-reduction technology for use in large-scale coal-fired power plants. Significant progress has been achieved in the research and development of this technology during its scaling up from 0.4 MW_th to 3 MW_th and 35 MW_th by the combined efforts of universities and industries in China. A prefeasibility study on a 200 MW_e large-scale demonstration has progressed well, and is ready for implementation. The overall research development and demonstration (RD&D) roadmap for oxyfuel combustion in China has become a critical component of the global RD&D roadmap for oxyfuel combustion. An air combustion/oxyfuel combustion compatible design philosophy was developed during the RD&D process. In this paper, we briefly address fundamental research and technology innovation efforts regarding several technical challenges, including combustion stability, heat transfer, system operation, mineral impurities, and corrosion. To further reduce the cost of carbon capture, in addition to the large-scale deployment of oxyfuel technology, increasing interest is anticipated in the novel and next-generation oxyfuel combustion technologies that are briefly introduced here, including a new oxygen-production concept and flameless oxyfuel combustion.