Micro Air Vehicles (MAVs) are defined as a class of vehicles with their larger dimension not exceeding 15 cm and weighing 100 gm. The three main approaches for providing lift for such vehicles are through fixed, rotating and flapping wings. The flapping wing MAVs are more efficient in the low Reynolds-number regime than conventional wings and rotors. Natural flapping flyers, such as birds and insects, serve as a natural source of inspiration for the development of MAV. Flapping wing design is one of the major challenges to develop an MAV because it is not only responsible for the lift, but also propulsion and maneuvers. Two important issues are addressed in this thesis: (1) an equivalent beam-type modeling of actual insect wing is proposed based on the experimental data and (2) development of the numerical framework for design and analysis of insect scale smart flapping wing. The experimental data is used for structural modeling of the blowfly Calliphora wing as a stepped cantilever beam with nine spanwise sections of varying mass per unit lengths, flexural rigidity (EI) and torsional rigidity (GJ) values. Natural frequencies, both in bending and torsion, are obtained by solving the homogeneous part of the respective governing differential equations using the finite element method. It is found that natural frequency in bending and torsion are 3.17 and 1.57 times higher than flapping frequency of Calliphora wing, respectively. The results provide guidelines for the biomimetic structural design of insect-scale flapping wings. In addition to the structural modeling of the insect wing, development of the biomimetic mechanisms played a very important role to achieve a deeper insight of the flapping flight. Current biomimetic flapping wing mechanisms are either dynamically scaled or rely on pneumatic and motor-driven flapping actuators. Unfortunately, these mechanisms become bulky and flap at very low frequency. Moreover, mechanisms designed with conventional actuators lead to high weight and system-complexity which makes it difficult to mimic the complex wingbeat kinematics of the natural flyers. The usage of the actuator made of smart materials such as ionic polymer metal composites (IPMCs) and piezoceramics to design flapping wings is a potential alternative. IPMCs are a relatively new type of smart material that belongs to the family of Electroactive Polymers (EAP) which is also known as “artificial muscles”. In this work, structural modeling and aerodynamic analysis of a dragonfly inspired IPMC flapping wing are performed using numerical simulations. An optimization study is performed to obtain improved flapping actuation of the IPMC wing. Later, a comparative study of the performances of three IPMC flapping wings having the same size as the actual wings of three different dragonfly species Aeshna Multicolor, Anax Parthenope Julius and Sympetrum Frequens is conducted. It is found that the IPMC wing generates sufficient lift to support its own weight and carry a small payload. In addition to the IPMC, piezoelectric materials are also considered to design a dragonfly inspired flapping wing because they have several attractive features such as high bandwidth, high output force, compact size and high power density. The wings of birds and insects move through a large angle which may be obtained using piezofan through large deflection. Piezofan which is one of the simple motion amplifying mechanisms couples a piezoelectric unimorph to an attached flexible wing and is competent to produce large deflection especially at resonance. Non-linear dynamic model for the piezoelectrically actuated flapping wing is done using energy method. It is shown that flapping angle variations of the smart flapping wing are similar to the actual dragonfly wing for a specific feasible voltage. Subsequently, a comparative study of the performances of three piezoelectrically actuated flapping wings is performed. Numerical results show that the flapping wing based on geometry of dragonfly Sympetrum Frequens wing is suitable for low speed flight and it represents a potential candidate for use in insect scale micro air vehicles. In this study, single crystal piezoceramic is also considered for the flapping wing design because they are the potential new generation materials and have attracted considerable attention due to superior electromechanical properties. It is found that the use of single crystal piezoceramic can lead to considerable amount of wing weight reduction and increase of aerodynamic forces compared to conventional piezoelectric materials such as PZT-5H. It can also be noted that natural fliers flap their wings in a vertical plane with a change in the pitch of the wings during a flapping cycle. In order to capture this particular feature of the wingbeat kinematics, coupled flapping-twisting non-linear dynamic modeling of piezoelectrically actuated flapping wing is done using energy method. Excitation by the piezoelectric harmonic force generates only the flap bending motion, which in turn, induces the elastic twist motion due to interaction between flexural and torsional vibrations modes. It is found that the value of average lift reaches to its maximum when the smart flapping wing is excited at a frequency closer to the natural frequency in torsion. Moreover, consideration of the elastic twisting of flapping wing leads to an increase in the lift force.