Diesel engine in-cylinder combustion processes have been studied using computational models with particular attention to spray development, vaporization, fuel/air mixture formation and combustion. A thermodynamic zero-dimensional cycle analysis program was used to determine initial conditions for the multidimensional calculations. A modified version of the time-dependent, three-dimensional computational fluid dynamics code KIVA-II was used for the computations, with a detailed treatment for the spray calculations and a simplified model for combustion. The calculations were used to obtain an understanding of the potential predictive capabilities of the models. It was found that there is a strong sensitivity of the results to numerical grid resolution. With proper grid resolution, the calculations were found to reproduce experimental data for non- vaporizing and vaporizing sprays. However, for vaporizing sprays with combustion, extremely fine grids are needed. Computations made with the coarse grid sizes that are typically used underpredict measured gas phase (vapor) penetration results substantially. This underprediction of spray penetration reduces the accuracy of combustion predictions greatly. A study was made of factors that cause the observed sensitivity of the results to the computational grid size. The spray drop size and the fuel vaporization rate were found to be key parameters. Models for the processes that influence these parameters such as atomization, vapor diffusion and condensation processes are discussed.