Computational fluid dynamics (CFD) of complex processes and complicated geometries embraces the transport of momentum, heat, and mass including the description of reaction kinetics and thermodynamics. The paper outlines the numerical models available for analyzing these processes and presents examples of such methodology. The unprecedented growth in computer capability has resulted in efficient simulations of most transport phenomena. The aerospace's interest in high-pressure turbulent combustion has created efficient computational tools for analyzing run-away-reactions in the process industries. Practical turbulence models, generalized thermodynamic properties, and extensive chemical kinetics data bases are currently used in three-dimensional, steady-state simulations. However, industrial needs have challenged CFD modelers to improve their flow solvers in order to simulate flows with more complicated physics, such as spray combustion, acoustic waves, transient start-up and shut-down, and flow instabilities. In addition, the practicality and efficiency of numerical simulations are highly dependent on the submodels employed, such as reaction mechanisms and turbulence models. There has been some progress in generalizing CFD tools, but more development is needed. Most of all, more high-quality and critical test data are required to validate the CFD simulations of complex processes. The laminar transport equations have been averaged by various means to locally describe both turbulent and multiphase flows. Spray combustion, stirred-tank reactors, fluidization of catalytic beds, and highly exothermic supercritical reactors are among the several validated examples, which illustrate today's technology. The designer's access to public-domain, open-source software offers powerful methodology for his use. Such software and the variety of available modeling techniques will be inventoried to demonstrate the scope of computational transport methodology. The current state of CFD models will be assessed to address the need for future research. (c) 2005 Elsevier Ltd. All rights reserved.