Flow separation incurs a large amount of energy loss and limits the performance of many flow-related devices (e.g., airfoils, diffusers, etc.). Researchers have been trying to mitigate or eliminate flow separation for over a century because of its large potential payoff in practical applications. Numerous active separation control strategies have been attempted on civil and military aircraft and underwater vehicles with varying degrees of success. However, most of the active control approaches are open-loop in nature because of their simplicity but are often time-consuming and expensive. This talk discusses two novel adaptive feedback control approaches designed to reattach a massively separated flow over a NACA airfoil with minimal control effort using piezoelectric synthetic jet actuators and various sensors for feedback. One approach uses an adaptive feedback disturbance rejection algorithm in conjunction with a system identification algorithm to develop a reduced-order dynamical systems model between the actuator voltage and unsteady surface pressure signals. The objective of this feedback control scheme is to suppress the pressure fluctuations on the upper surface of the airfoil model, which results in reduced flow separation, increased lift, and reduced drag. A second approach leverages various flow instabilities in a nonlinear fashion to maximize the lift-to-drag ratio using a constrained optimization scheme - in this case using a static lift/drag balance for feedback. Detailed experiments are described to elucidate the baseline uncontrolled and controlled flow physics, and various technical challenges are addressed and discussed in detail.