Recent advances in the description of the dynamics and geometry of surfaces of premixed flames under the influence of stretch as manifested by aerodynamic straining, flame curvature, and flame/flow unsteadiness are reviewed via the G-equation formulation, where G = constant is a level surface in a flow field. The discussion first treats the flame as a structureless surface that propagates into the fresh mixture with a constant velocity— the laminar flame speed, and the phenomena of cusp formation and volumetric burning rate augmentation through wrinkling are demonstrated. It is then shown that by considering the effects of stretch on the flame structure, and by allowing for mixture nonequidiffusion, the flame responses, especially the flame speed, can be quantitatively as well as qualitatively modified. By using the stretch-affected flame speed, we then describe the phenomena of cusp broadening, of tip opening of the Bunsen flame, and of the intrinsic hydrodynamic, body-force, and diffusional-thermal modes of flamefront cellular instabilities. The review closes with suggestions for further research.