A survey of the characteristics and predictions of the different theoretical models of the spread of flames over the surface of a solid combustible in opposed or concurrent oxidizing flows shows that, at present, there is a good understanding of what are the controlling mechanisms of the flame spread process andl of what is the necessary formulation to develop a rigorous analysis of the phenomenon. It also shows, however, that the problem is very complicated and difficult to solve mathematically particularly if an analytical solution is sought, and that this complexity is what has prevented so far the development of an analysis capable of describing accurately the flame spread process under realistic conditions where material properties, finite rate kinetics, turbulence and radiation effects can determine the characteristics of the process. Although some of the analyses presently available are capable of predicting quantitatively or at least qualitatively rates of flame spread under certain limiting conditions, it appears that the development of a rigorous numerical analysis will be necessary to predict accurately the flame spread process under varied material and environmental conditions.