Many processes of interest in chemical engineering are yet beyond the reach of a numerical solution in a practical sense. For such processes, creative modeling by means of idealizations and approximations and innovative methods of solution may be needed. Homogeneous combustion, because of extreme temperature gradients, developing flow, turbulent. convection of momentum, energy, and species, thermal radiation, and a seemingly unlimited array of free-radical reactions, each with a complex and uncertain dependence on temperature, exemplifies such a process. Guidelines for such modeling have been identified from the accumulative experiences of a long sequence of research on one form of combustion, namely that stabilized primarily by thermal radiation.