Flapping propulsion is widely adopted by many natural flyers/swimmers, including insects, birds, fishes, and marine mammals. It offers an attractive alternative to conventional propulsion methods for future bio-inspired aerial/underwater systems.However, due to lack of effective technology of studying the highly complex propulsor morphing kinematics and its associated aero/hydrodynamics, achieving biological levels of aero/hydro-performance in bio-inspired flapping propulsor design has proven elusive.Here, an integrated experimental and computational methodology has been developed to systematically study the flapping propulsion system in nature. The goal is to advance the fundamental knowledge of biological fluid dynamics in animal flight/swimming, and provide guidance for future optimal designs of bio-inspired flapping propulsors.The current dissertation consists of two parts, tools development and analysis of propulsion systems. In the first part, the integrated methodology is introduced, and the corresponding major contributions of the work are: (1) a highly versatile and accurate jointbased surface reconstruction method is developed to quantify the propulsor flexion and body kinematics of animals in free flight/swimming; (2) a spherical-coordinates-based singular value decomposition (SSVD) method is developed to perform low dimensional morphology analysis of flapping propulsors in nature; (3) an immersed boundary method for deformable attaching bodies (IBM-DAB) is developed to handle direct numerical simulations (DNS) in some extreme situations which are commonly exist in nature, including solid body with sharp edge and with deformable attaching membrane bodies; (4) ii a highly efficient gradient-based parallel curve searching optimizer is developed to explore design space of flapping propulsors.In the second part, the aforementioned integrated approach is applied to study several problems. We first investigate the optimal configurations of several morphological parameters, which control the dynamic camber and twisting of the propulsors, on aerodynamic performance using simplified canonical models. Optimizations of dynamic camber formation of 2D pitching-plunging plates and dynamic twisting of 3D pitchingrolling plates are performed. It is found that the morphological parameters play important roles in the plate aerodynamic performance and wake structures. Comparing to completely rigid plate, the thrust production and propulsive efficiency of optimized plates can be improved up to 29.1% and 43.1%, respectively. The associated flow mechanisms are found to be the improved strength and attachment of leading-edge vortex (LEV).Next, the integrated approach is used to study the complex morphing propulsor kinematics and the associated aero/hydrodynamics of natural flyers/swimmers in relatively simple motions, such as hovering and fast swimming. The SSVD analysis of the forewing motion of a hovering dragonfly reveals that the complicated wing motion can be represented by a low dimensional model contains two ...