Better methods of analyzing combustion dynamics in internal combustion (IC) engines are needed as a consequence of increasing demands for greater thermal efficiency, lower pollutant output, and improved fuel flexibility. In response to these needs, both improved diagnostic devices and computational techniques are being developed. Together, these developments may lead to a more detailed understanding of the combustion process. In particular, advanced numerical simulation techniques, may ultimately produce the capability of calculating both the spatial and temporal evolution of the fuel/air mixture for the IC engine cycle as well as the combustion process itself. During the last several years, a number of publications have appeared, describing both one-dimensional and two-dimensional, transient computer codes which indicate steady progress toward the goal of a computational tool which is capable of making performance predictions at a reasonable cost. In the present paper, we briefly review this progress from the point of view of establishing the current predictive capability and indicate both the capabilities and limitations which currently exist. Areas requiring further improvements are pointed out and approaches currently envisioned for resolving computational difficulties are discussed.