Oxy-fuel combustion of pulverized fuels (PF), as a promising technology for CO2 capture from power plants, has gained a lot of concerns and also advanced considerable research, development and demonstration in the past years worldwide. The use of CO2 or the mixture of CO2 and H2O vapor as the diluent in oxy-fuel combustion, instead of N-2 in conventional air-fuel combustion, induces significant changes to the combustion fundamentals, because of the great differences in the physical properties and chemical effects of the different diluents. Therefore, some fundamental issues and technological challenges need to be properly addressed to develop oxy-fuel combustion into an enabled technology. Computational Fluid Dynamics (CFD) modeling, which has been proven to be a very useful and cost-effective tool in research and development of conventional air-fuel combustion, is expected to play a similarly vital role in future development of oxy-fuel combustion technology. The paper presents a state-of-the-art review and an in-depth discussion of PF oxy-fuel combustion fundamentals and their modeling, which underpin the development of this promising technology. The focus is placed on the key issues in combustion physics (e.g., turbulent gas-solid flow, heat and mass transfer) and combustion chemistry (e.g., pyrolysis, gas phase combustion and char reactions), mainly on how they are affected in oxy-fuel conditions and how they are modeled and implemented into CFD simulations. The system performance of PF oxy-fuel combustion is also reviewed. Finally, the current status of PF oxy-fuel combustion fundamentals and modeling is concluded and the research needs in these regards are suggested. (C) 2015 Elsevier Ltd. All rights reserved.