A review of research on the effects of gravity on combustion processes is presented, with an emphasis on a discussion of the ways in which reduced-gravity experiments and modelling has led to new understanding. Comparison of time scales shows that the removal of buoyancy-induced convection leads to manifestations of other transport mechanisms, notably radiative heat transfer and diffusional processes such as Lewis number effects. Examples from premixed-gas combustion, non-premixed gas-jet flames, droplet combustion, flame spread over solid and liquid fuels and other fields are presented. Promising directions for new research are outlined, the most important of which is suggested to be radiative reabsorption effects in weakly burning flames.