There is great interest in small aircraft known as Micro Air Vehicles and mini Unmanned Air Vehicles due to the wide range of possible applications. This article reviews recent work that aims to exploit the flexibility of the wing structure in order to increase lift and thrust, and delay stall. Wing flexibility has often been considered to be unwanted for large conventional aircraft and measures are taken to limit the deformation. In contrast, very small aircraft flying at low speeds are not necessarily subject to the same limitation. This approach is only applicable to small aircraft because the frequencies of the wing structure and fluid flow instabilities are close to each other. Consequently, small amplitude and high-frequency motions will be considered. We first start with rigid airfoils and wings in forced plunging motion, which mimics the bending oscillations. The main advantage of this approach is the freedom to vary the frequency within a wide range. Two mechanisms of high-lift production on the oscillating rigid airfoils are discussed. In the first one, leading-edge vortex dynamics and different modes of vortex topology play an important role on the time-averaged lift and thrust at post-stall angles of attack. Existence of optimal frequencies and amplitudes are demonstrated, and their relation to other phenomena is discussed. In the second mechanism of high-lift, trailing-edge vortex dynamics leads to bifurcated/asymmetric flows at pre-stall angles of attack. Deflected wakes can lead to time-averaged lift coefficients higher than those for the first mechanism. Some aspects of lift enhancement can be sensitive to the airfoil shape. For three-dimensional finite wings, lift enhancement due to the leading-edge vortices and existence of optimal frequencies are similar to the two-dimensional case. Vortex dynamics of the leading-edge vortex and tip vortex is discussed in detail. Leading-edge sweep is shown to be beneficial in the reattachment of the separated flows over oscillating wings. Oscillating flexible wings can provide much higher lift coefficient than the rigid ones. Amplitude and phase variation in the spanwise direction result in much stronger leading-edge and tip vortices. Self-excited vibrations of flexible wings, including membrane wings, can excite shear layer instabilities, and thus delay stall and increase lift. Finally, thrust enhancement or drag reduction can be achieved by employing chordwise and spanwise flexibility. The effects of wing flexibility on the vortices and thrust/drag are discussed in relation to the characteristics of wing deformation.