This paper seeks to bring together a number of results pertaining to the interaction of pressure waves with premixed combustion fronts. Some of the earlier results concerning low–speed flames and acoustics are set in context with some of the later work, which is still being developed and which takes compressibility into account to a much greater extent. The interaction of low–speed flames with steep pressure drops shows a possible mechanism for flame extinction, and the interaction with steep pressure rises indicates conditions for rapid flame acceleration to fast convection–reaction driven deflagrations. This work demonstrates that the transient nature of fast flames, with their corresponding acoustic and reactive acoustic zones due to temperature singularities (blow up) occurring near the driving piston of such deflagrations, is very sensitive to imposed pressure disturbances. In a separate section at the end of this paper, we address the question of the amplification of long–wavelength acoustic waves reflected from fast deflagrations, where the entropy change across such fronts is significant, but where the structure of the deflagration is uncertain.