Flapping of an insect wing can be broadly separated into sweeping, elevating, and rotational motions. The sweeping motion generates forward velocity, and the rotational motion imposes an appropriate angle of attack; both are vital to lift generation. However, the purpose of elevating motion in insect flight remains unclear. In this paper, the aim is to better understand the effects of elevating motion to lift generation and vortex structure development when rigid wings are subjected to three-dimensional simple harmonic motion and hovering hawkmoth flapping motion. Both experimental and numerical techniques are used, and results show that, among the different types of simple harmonic motions considered here, only figure-of-eight motions at a relatively low midstroke angle of attack (25 deg) outperform flapping motions without elevating motion. In this case, lift is enhanced by approximately 11% with insignificant cost to hovering efficiency. The lift enhancement could be attributed to rapid growth of the leading-edge vortex, due to an increase in instantaneous angle of attack when the wing elevates downward during midstroke. For the hawkmoth motion, a small elevating motion has minimal aerodynamic effects, whereas a large one causes reduction in lift due to detachment of the leading-edge vortex from the wing surface. Generally, elevating motion affects lift and power coefficients via four mechanisms: Alteration of instantaneous angle of attack, introduction of radial force component, wake capture, and early shedding of leading-edge vortex. Although elevating motion confers a significant lift enhancement to specific sets of flapping-wing kinematics, it is generally detrimental to flight performance.