Combustion is currently responsible for 80-90% of the power production worldwide, and is expected to remain the major energy conversion process for the foreseeable future.  Thus, it is essential that improvements be made in the design and operation of practical combustors.  Traditional engineering has made major advancements in engine design, but future stringent efficiency and emission requirements will be achieved only if the processes occurring in engines could be described and understood in detail.  Such understanding can only be achieved in low-dimensional reacting environments in which the various physical and chemical processes affecting combustion can be isolated and independently controlled.  Thus, such fundamental studies can yield models that could be used for the detailed and reliable modeling of engines.  In this presentation two examples will be used to endorse this approach: (1) The phenomenon of “flammability limits” for gaseous flows, and (2) The phenomenon of flame extinction for reacting dusty flows in which solid particles interact with gaseous flames.  In both cases the coupling of fluid mechanics, molecular transport, and chemical kinetics will be discussed.