The problem of ignition stability arises in the case of the action of intense external heat stimuli when, resulting from the cut-off of solid substance heating, momentary ignition is followed by extinction. Physical pattern of solid propellant ignition is considered and ignition criteria available in the literature are discussed. It is shown that the above mentioned problem amounts to transient burning at a given arbitrary temperature distribution in the condensed phase. A brief survey of published data on experimental and theoretical studies on ignition stability is offered. The comparison between theory and experiment is shown to prove qualitatively the efficiency of the phenomenological approach in the theory. However, the methods of mathematical simulation as well as those of experimental studying of ignition phenomenon, especially at high fluxes, need to be improved.