In this talk I'll give a summary of the work I did during my PhD. The first part of the talk will be concerned with premixed flames propagating against a parallel flow. I'll discuss how the thick flame asymptotic limit can lead to an enhanced flame propagation speed in an effect analogous to the classical Taylor dispersion problem. The relevance of this result (obtained for a laminar flame) to turbulent combustion will be discussed. Then I'll talk about the effects of thermal expansion and gravity on triple flames. These structures arise where there is a stratification in the concentrations of fuel and oxidiser in a reactive mixture.