Recent advances in the understanding of the structure, dynamics, and geometry of laminar premixed flames under the influence of stretch, as manifested by aerodynamic straining, flame curvature, and flame/flow unsteadiness, are reviewed and presented in a tutorial manner. The discussion first treats the flame as a structureless surface which 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 flame 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. Additional topics covered include forced and intrinsic oscillatory flame dynamics, and quantitative extraction of the global flame parameters represented by the activation energy, the Markstein length, and the Lewis number.