The problem of modeling combustion within internal combustion engines is considered. A method is explained to evaluate the comprehensiveness, detail and predicting capability of a model. It consists of considering the equations for the most comprehensive and detailed model and in making successively more restrictive assumptions, thus getting progressively less detailed models. Particular attention is paid to the reasons for the assumptions, how they influence the accuracy of a model, and what basic information is missing. In so doing, the most detailed of the available models, and their predictive capabilities and limitations, are introduced. They include models for reciprocating and rotary engines, with uniform and stratified charges from dual carburetion and direct fuel injection. Examples of their results are given. One of them has been available since 1971, and another one is currently and fruitfully employed to aid the development of a production engine. Also introduced are more advance models presently under development and their applications. The equations of the most common and least detailed models are derived from the most general equations, thus evidencing their inherent limitations.