There has been a surge of interest in the development of micro-air vehicles (MAVs) and autonomous underwater vehicles (AUVs). These technologies provide low-cost, compact, and maneuverable means for terrain mapping, search and rescue missions, and reconnaissance. With the push to build smaller MAVs and AUVs, the importance of the flapping wing design increases, as these wings are capable of generating more force per surface area than any other leading MAV or AUV design. In this work, we study flapping wing propulsion by employing a Cyber-Physical approach to examining oscillating airfoils. Cyber-Physical Fluid Dynamics, or CPFD, is a technique that combines a physical experiment with a computer-controlled, force-feedback system, allowing for us to virtually add any kinematics or forces to our object of interest in real-time. This greatly expands the achievable studied parameter space compared to traditional experimental techniques. In the first part of this work, we will examine an actively-heaving, passively-pitching airfoil. We specify the heaving (transverse to incoming flow) motion, while the pitching (rotational) motion is passively generated through fluid forces and virtual torsion springs implemented with CPFD. Introducing passive dynamics would eliminate the necessity of another actuator, decreasing complexity, weight, and cost in the design of MAVs or UAVs. We also study a sports-mimetic, sail-flicking-inspired motion called hybrid-heave. This motion is known by sailors to greatly bolster travel speeds, and we uncover the vortex dynamics that drive the increased propulsion. In the latter half of this work, we study a heaving and pitching, self-propelled airfoil. Unlike traditional tethered studies, a self-propelled airfoil freely accelerates in the travel direction, accurately coupling the travel speed to the forces generated. Self-propulsion has been historically challenging to implement with traditional experimental techniques; however, the force-feedback system of CPFD allows for the airfoil’s velocity to dynamically change in response to the instantaneous forces generated. We examine both a symmetrically and asymmetrically flapping NACA 0012 and discover the oscillation parameters that optimize cruising velocity, efficiency, and lift generation. We also focus on identifying the underlying vortex dynamics that propel these optimal conditions.