The biomimicking and understanding of the dynamics of insect flyers is important in developing agile and efficient MAVs. The present study is based on the development of dragonfly inspired MAV and investigation of its motion characteristics. Initially, a tethered two-winged MAV model is constructed, composing of two flapping wings, a flapping mechanism, a chassis, and an external power supply with a function generator. The wings are fabricated with composite stiffeners and membrane. The material of the wings consists of carbon nanotubes (CNTs)/polypropylene (PP) nanocomposite and low density polyethylene (LDPE). The wings are thus lightweight, thin, flexible, and can generate large amplitude bending-twisting motion. The flapping mechanism is constructed with a cantilever type piezoelectric actuator, a mediator mechanism having CNTs/PP nanocomposite flexure joints, and carbon fiber/epoxy composite linkages. The assembled two-winged MAV model has a total mass, body length, wingspan, and aspect ratio of 0.61g, 60.46mm, 90.14mm, and 10.06, respectively. The characteristic flapping frequency of the model is 20Hz, as compared to the wingbeats (or characteristic frequency) of 27.53Hz of an actual dragonfly species, i.e., the Anax Parthenope Julius. Measured via digital image correlation (DIC) technique, the fabricated wings exhibit a bending dominated motion during downstroke as well as upstroke. The combined design of flapping wings and flexure joint mechanism is also computationally studied for their structural dynamic characteristics (performed using ANSYS). The first resonance mode or the characteristic frequency, at which the wings have highest deflections, is 17.25Hz. The flexure mechanism is able to generate very large wing deflections (maximum deflection 22.7mm at wing tip) with a sinusoidal heaving input excitation of very small amplitude (0.1mm given at the actuator attachment location). This is useful to generate higher aerodynamic forces and improve efficiency. The maximum stresses and strains are found at flexure-rigid link and wing stiffener attachment, respectively. Finally, a dragonfly-inspired four-winged MAV is developed. It consists of two pairs of nanocomposite wings with independently actuated flapping mechanisms. Like a natural dragonfly, the forewing and hindwing pairs can be controlled independently and operated at different characteristic frequencies as well as relative phase angles.