Three-phase slurry bubble column reactors are used in a wide variety of biological and chemical operations. This work is a comprehensive review of the mathematical modeling of such reactors for the Fischer-Tropsch (F-T)synthesis as applied to indirect coal liquefaction. The salient features of the F-T slurry bubble column reactors are described, and the fundamental mass transfer and kinetic rate processes that are needed to model the reactor performance are discussed. A brief description of the F-T chemistry, including principal F-T reactions, properties of commonly used F-T catalysts, and the Schulz-Flory distribution, is also given. All of the mathematical models for the F-T slurry process that have been developed to date are presented in enough detail to highlight the basic relations as well as the implicit assumptions. The refinements introduced by different workers are emphasized, as well as the numerical results obtained from these models either in the perspective of comparison with experimental data or in relation to design implications. The controversy surrounding the importance of relative mass transfer resistance in F-T slurry reactors is discussed. It is concluded that none of the available models includes enough details in relation to hydrodynamics, kinetics, and F-T chemistry to provide a reliable base for either prediction of conversion or optimum reactor design. Suggestions are given to develop such a comprehensive model, and the particular features that must be included in its formulation are elaborated.