Development and application of comprehensive, multidimensional, computational combustion models are increasing at a significant pace across the world. While once confined to specialized research computer codes, these combustion models are becoming more readily accessible as features in commercially available computational fluid dynamics (CFD) computer codes. Simulations made with such computer codes offer great potential for use in analyzing, designing, retrofitting, and optimizing the performance of fossil-fuel combustion and conversion systems. The purpose of this paper is to provide an overview of comprehensive combustion modeling technology as applied to fossil-fuel combustion processes. This overview is divided into three main parts. First, a brief review of the state-of-the-art of the various components or submodels that are required in a comprehensive combustion model is presented. These submodels embody mathematical and numerical representations of the fundamental principles that characterize the physico-chemical phenomena of interest. The submodel review is limited to those required for characterizing non-premixed, gaseous and pulverized coal gasification and combustion processes. A summary of the submodels that are available in representative computer codes is also presented. Second, the kinds of data required to evaluate and validate the predictions of comprehensive combustion codes are considered. To be viewed with confidence, code simulations must have been rigorously evaluated and validated by comparison with appropriate experimental data, preferably from a variety of combustor geometries at various geometric scales. Three sets of validation data are discussed in detail. Two sets are from the highly instrumented, pilot-scale combustor called the controlled profile reactor (CPR) (one natural gas-fired and one coal-fired), and the other set is for a full-scale, corner-fired 85 MW, utility boiler. Third, representative applications of comprehensive combustion models are summarized, and three sets of model simulations are compared with experimental data. The model simulations for the three test cases were made using two commonly used, CFD-based computer codes with comprehensive combustion model features, PCGC-3 and FLUENT 4.4. In addition to the standard version of FLUENT, predictions were also made with a version of FLUENT incorporating advanced submodels for coal reactions and NO pollutant formation.