The highly localized and exothermic chemical reactions occurring in combustion processes are associated with a significant increase in temperature and consequently a drop in density. The gas expansion has a pronounced effect on flame dynamics which is the topic of this presentation. In premixed flames the gas expansion gives rise to an intrinsic hydrodynamic instability which, except for small-scale laboratory flames, overcomes the stabilizing influences of diffusion. This leads to corrugated structures with relatively large transverse dimensions that propagate at a speed much larger than the laminar flame speed. In diffusion flames, on the other hand, thermal expansion does not play such a crucial role. Cellular and polyhedral flames, oscillations, and other modes of instabilities are primarily driven by diffusive-thermal effects with density variations slightly modifying the growth rate. Edge-flames which have complex structures consisting of three branches, lean and rich premixed segments with a diffusion flame positioned nearly along the stoichiometric surface, exhibit various form of instabilities. The most distinct of these is oscillations, where the edge of the flame moves back and forth dragging along the trailing diffusion flame. Results concerning the effect of thermal expansion on the dynamics of edge-flames will also be discussed.