The combustion process in
IC
engines is characterized by complex multiphase, turbulent reacting flows that span multiple regimes, including premixed flame propagation, mixing‐controlled burning, and chemical kinetics‐controlled processes. For predictive modeling, these processes must be represented with accurate mathematical models and numerical schemes, and this chapter reviews the current state of the art. Zero‐dimensional models based on thermodynamic cycle analysis can require extensive model constant tuning. Multidimensional computational fluid dynamics (
CFD
) modeling reduces the amount of model calibration required. However, submodels must still be used to describe processes that occur on time and length scales too small to be resolved in a simulation, but the inclusion of more and more detail has been made possible by recent dramatic increases in computer power. It is now widely recognized that engine
CFD
simulations can offer significant advantages in the engine development process, including being able to provide detailed in‐cylinder information, which is often inaccessible in experiments. Other advantages over engine experiments include lower cost, the ability to explore wider ranges of parameter variation, and the ability to separate and monitor individual processes. In addition, when coupled with optimization tools, new design concepts can be discovered using multidimensional modeling, as described with examples in this chapter.