In this thesis, the aerodynamic challenges in flapping wing flight are addressed. In particular, the effects of different wing kinematics, flexibilities, and planforms on the the leading edge vortex development and aerodynamic performance are investigated. In a first part, we experimentally optimise the kinematics of a flapping wing system in hover with the objective to maximise the lift production and hovering efficiency. Additional flow field measurements are performed to link the vortical flow structures to the aerodynamic performance for the optimal kinematics. We obtain kinematics which promote the formation of a strong leading edge vortex and yield high lift coefficients, and kinematics which promote leading edge vortex attachment and are more power efficient. We identify the shear layer velocity as a scaling parameter for the growth of the vortex and its impact on the aerodynamic forces. The experimental data agree well with the scaling, making the shear layer velocity a promising metric to quantify and predict the aerodynamic performance of the flapping wing hovering motion for the design and control of micro air vehicles. In a second part, a novel bio-inspired membrane wing design is introduced, and used to study the fluid-structure interactions of flapping membrane wings. We find optimal combinations of the membrane properties and kinematics that out-perform their rigid counterparts both in terms of increased stroke-average lift and efficiency, and characterise them with an aeroelastic number. Flow field measurements around the membrane wings reveal that the leading edge vortex formation is suppressed at lift and efficiency optimal aeroelastic conditions. These results demonstrate that a leading edge vortex is not always required to generate high lift in flapping wing flight. If the membrane wings become too flexible, the flow separates over the high curvature of the wing, and the wing experiences great losses in lift and hovering efficiency. These findings explain the flight behaviour of bats which adapt either their wing's angle of attack, stiffness, or flight velocity. We suggest using active flow control for artificial membrane wing vehicles, and the leading and trailing edge angles as indicators for the flow state to maintain optimal aeroelastic conditions in flight. In a third and final part, hawk moth wing shapes are collected and their aerodynamic performance, and leading edge vortex formation compared to flat and rectangular wings. Three-component flow field measurements over the full span and aerodynamic force recordings are conducted for scaled wing models on a robotic flapping wing system. We investigate if the morphology of hawk moth wings could have evolved to accommodate the formation of a strong and coherent leading edge vortex for aerodynamic benefits. While all wings have the same surface area and aspect ratio, the rectangular wing produces only half the lift and drag coefficients compared to the hawk moth wings. The difference in force production is also reflected in the leading edge vortex formation on the wings. At mid-span the vortex lifts off of the wing on the rectangular planform. On the hawk moth wing planform, the local chord length is adapted to allows the leading edge vortex to expand over the full wing span. The higher wing loading improves the flight control and escape capabilities of flapping wing fliers, and allows the smaller, high aspect ratio wings of the hawk moth to produce sufficient