In this study we examine theoretically the structure of a simple one-dimensional spray diffusion flame. The analysis is carried out along two complementary routes: an asymptotic approach, that treats the limiting behaviors of fast vaporization followed by fast chemical reaction and illustrates the various physical mechanisms involved in the complex multi-phase field, and a numerical approach that validates and extends the solution to arbitrary parameter values. The results emphasize the importance of heat and mass transfer rates, the supply conditions, the droplet loading, the size distribution of the droplets in the spray and the effects of volumetric heat loss. Particular attention is given to the conditions for flame extinguishment and those effects that may promote or delay extinction.