Oxy-fuel combustion is a promising technology for carbon capture and storage (CCS) from large point sources. In particular, fluidized bed (FB) boilers represent one of the power generation technologies capable of utilizing the oxy-fuel concept. This paper reviews the published material on the key aspects of oxy-fuel circulating FB, including the boiler heat balance, heat transfer mechanisms, furnace hydrodynamics, and the mechanical and chemical mechanisms of the process. In particular, it demonstrates the challenges of utilizing high inlet O-2 concentrations in the oxy-fuel process in fluidized beds. This requires significantly more efficient gas-particle clean-up technology (especially for Cl with perhaps 19% retention and Hg with 2.15 mu g/m(3) in flue gases), high circulating solids flux and, hence, significant heat extraction outside the furnace (up to 60% of the boiler's total heat extraction). Scale-up of oxy-fuel CFB technology can partially compensate for the energy penalty from air separation by furnace downsizing when operating at high inlet O-2 concentrations. Critically, while there are numerous measurement campaigns and corresponding models from the pilot and, to a lesser extent, industrial scale, the paper endeavors to answer the questions about what information taken from such experimental campaigns is reliable, useful for future design, and for scale-up.