Oxy-coal combustion is one of the leading technologies for carbon capture and storage. This paper presents a review of the opportunities and challenges surrounding the development of oxy-coal combustion models and discusses historical and recent advances in specific areas related to computational fluid dynamics (CFD), including char oxidation, radiation, pollutant formation and removal (Hg, NOx and SOx), and the impact of turbulence. CFD can be used to assess and optimise full-scale retrofit designs and to provide data on matching air-fired heat duties. In addition, CFD can also be used to improve combustion efficiency and identify potential reductions in corrosion, slagging, fouling and trace pollutant emissions. Transient simulations are becoming more computationally affordable for coal combustion, providing opportunities for model development. High concentrations of CO2 and H2O in oxy-coal can influence chemical kinetic rates, burnout and ash properties. The modelling can be improved by incorporating detailed kinetic mechanisms of gasification reactions. In addition, pollutant formation and removal mechanisms must be understood during oxy-coal firing to aid the selection of flue-gas cleaning strategies. Radiative heat transfer using spectral models for gaseous properties may be necessary in oxy-coal modelling because CO2 and H2O molecules have strong emission bands. Finally this review provides a coherent near-term and long-term oxy-coal specific CFD sub-models development strategy to simulate the complex oxy-coal combustion processes, heat transfer and pollutant emissions in power generation systems. (C) 2010 The Institution of Chemical Engineers. Published by Elsevier B.V. All rights reserved.