Abstract Fluidized-bed coal combustion has become an established and proven technology for the production of energy from high sulfur and low rank coals in an economically and environmentally acceptable mode. For proper design, scale-up and economic evaluation of industrial plants, a good understanding of the underlying principles of chemical kinetics and fluid mechanics governing the operating features of fluidized-bed combustors is essential. The hydrodynamics, combustion and sulfur retention kinetics, and heat transfer involved in such operations is known to be intricate. Most of the available and relevant information pertaining to the mathematical modelling of fluidized-bed coal combustors with sulfur retention is reviewed in this article. Details of some mechanistic models are given, while a brief description is included of others with a view to present to the reader the total picture and most up-to-date state of the art. This review concentrates most heavily on the mathematical modelling details of fluidized-bed coal combustors. For additional supplementary information, the reviews on coal devolatilization and combustion, heat transfer, and component design must also be consulted, some of which are referenced here.