We outline the rationale for using combustion techniques to economically synthesize valuable nanopowders, including mixed oxides, non-oxides, fullerenes, and nanotubes. Here "combustion" includes many exothermic reactive systems in which the "fuel" is not a hydrocarbon and the oxidizer is not O-2(g), as has also become the norm in the fields of chemical rockets and chemical lasers. Recent theoretical and experimental research studies have clarified many of the fundamental physical issues (e.g., Brownian coagulation, surface-energy-driven sintering, thermophoretic transport, etc.) necessary for the design of larger scale aerosol synthesis reactors and the harvesting/controlled deposition of particles. However, the prediction of "chemical nucleation rates" remains especially elusive. Specifically, even when the chemistry of precursor pyrolysis, oxidation, or hydrolysis is established, there remains the fundamental issue of how stable embryonic particles are actually formed and grow; i.e., what is the nanoparticle "birth rate" and how "large" are the "babies"? More generally, a multivariate description of the nanoaerosol population is required, and we outline recent advances in the simulation of such multivariate populations using systematic moment methods that are sufficiently general and articulate well with a computational fluid dynamics approach to the overall aerosol reactor design/ optimization/control. Of course, the control of flame-synthesized nanoparticle reactors will also require online, real-time probe measurements, often in "hostile" (high temperature, corrosive, etc.) environments. Extending the possibilities inherent in time-resolved laser-induced incandescence (TR-LII) is one of several attractive options, and we conclude with a summary of some recent relevant work/trends/prospects.