We measure the wing kinematics and morphological parameters of seven freely hovering fruitflies and numerically compute the flows of the flapping wings. The computed mean lift approximately equals to the measured weight and the mean horizontal force is approximately zero, validating the computational model. Because of the very small relative velocity of the wing, the mean lift coefficient required to support the weight is rather large, around 1.8, and the Reynolds number of the wing is low, around 100. How such a large lift is produced at such a low Reynolds number is explained by combining the wing motion data, the computed vortical structures, and the theory of vorticity dynamics. It has been shown that two unsteady mechanisms are responsible for the high lift. One is referred as to "fast pitching-up rotation": at the start of an up-or downstroke when the wing has very small speed, it fast pitches down to a small angle of attack, and then, when its speed is higher, it fast pitches up to the angle it normally uses. When the wing pitches up while moving forward, large vorticity is produced and sheds at the trailing edge, and vorticity of opposite sign is produced near the leading edge and on the upper surface, resulting in a large time rate of change of the first moment of vorticity (or fluid impulse), hence a large aerodynamic force. The other is the well known "delayed stall" mechanism: in the mid-portion of the up-or downstroke the wing moves at large angle of attack (about 45 deg) and the leading-edge-vortex (LEV) moves with the wing; thus, the vortex ring, formed by the LEV, the tip vortices, and the starting vortex, expands in size continuously, producing a large time rate of change of fluid impulse or a large aerodynamic force. C 2015 AIP Publishing LLC. [http://dx.dynamic stall vortex (they called it the leading edge vortex, LEV) did not shed in a downstroke or upstroke, even if the wing traveled more than five chord lengths in a downstroke. Their analysis of the momentum imparted to the fluid by the vortex wake showed that the LEV could produce enough lift for weight support. The above studies identified delayed stall (or maintaining the LEV on the wing) as a high-lift mechanism of insects. This was confirmed by subsequent experimental and numerical studies on rotating and flapping wings (e.g., Refs. 6-15). Furthermore, in these studies, 6-15 the development of the LEV was studied in detail and how the LEV attachment was maintained was explained.The wing stroke of an insect is typically divided into four portions: two translations (upstroke translation and downstroke translation) and two rotations around stroke reversal (pronation and supination). 7,16 The above delayed stall mechanism operates during the translational phases. 5,6 Dickinson et al. 7 explored the rotational phases by measuring the aerodynamic forces of a dynamically scaled model fruitfly. On the basis of wing kinematics measured in tethered fruitflies, they assumed the following wing motion pattern: the translational velocity varied accor...