Insects flap and twist their wings to stay aloft, to dart forward, to turn, and to hover. It is the swirls of air stirred by a flapping wing that generate an insect's lift and thrust. To understand how insects fly, it is necessary to understand the dynamics of unsteady airflows created by a flapping wing, which is significantly different from the steady airflows around a classical airfoil. Although the aerodynamics of a steady airfoil has been well understood for almost a century, it is only recently, with the advance of new experiments, computations, and analyses, that scientists have began to unravel some of the mysteries of unsteady aerodynamics.