Insect and bird size drones-micro air vehicles (MAV) that can perform autonomous flight in natural and man-made environment and hence suitable for environmental monitoring, surveillance, and assessment of hostile situations are now an active and well-integrated research area. Biological flapping-flight system design that has been validated through a long period of natural selection offers an alternative paradigm that can be scaled down in size, but normally brings lowspeed aerodynamics and flight control challenges in achieving autonomous flight. Thus mimetics in bioinspired flight systems is expected to be capable of providing with novel mechanisms and breakthrough technologies to dominate the future of MAVs. Flying insects that power and control flight by flapping wings perform excellent flight stability and manoeuvrability while steering and manoeuvring by rapidly and continuously varying their wing kinematics. Flapping wing propulsion, inspired by insects, birds and bats, possesses potential of high lift-generating capability under lowspeed flight conditions and may provide an innovative solution to the dilemma of small autonomous MAVs. In this study, with a specific focus on robustness strategies and intelligence in insect and bird flights in terms of morphology, dynamics and flight control, we present the state of the art of flying biomechanics in terms of flapping wing aerodynamics, flexible wing and wing-hinge dynamics, passive and active mechanisms in stabilization and control, as well as flapping flight in unsteady environments. We further highlight recent advances in biomimetics of insect-inspired flapping MAVs in concern with wing design and fabrication.