Diffusion Flames, the term given to combustion of non-premixed fuel and oxidizer, are common in many applications like furnaces and diesel engines and are also relevant to "solid propellant rockets" - the theme of this workshop. In this talk a general asymptotic theory for diffusion flames will be presented. In the limit considered, the chemical activity is confined to a thin zone which, when viewed from the much larger diffusion scale, is a moving two-dimensional sheet. The formulation is not restricted to any particular configuration and applies to conditions extending from complete combustion down to extinction. The detailed structure of the reaction zone yields jump conditions that permit full determination of the combustion and flow fields on both sides of the reaction sheet as well as the instantaneous location of the sheet itself. Specific examples will then be discussed with particular emphasis given to the onset of flame front oscillations.and the development of cellular structures.