Biological flapping wing flyers achieve flight maneuverability and efficiency in low speed flight environments that has not been replicated by man-made flyers. Micro Air Vehicle (MAV) design goals are to develop flyers that maintain flight in environments that biological flyers excel in which includes low speeds, hovering, and urban settings. This flight is characterized by flow phenomena that are not well understood such as: flow separation and vortical flow. The goal of this study is to perform a literature review about the aerodynamics of flapping flight and discuss the application to MAV design. The study will evaluate the design initiatives of MAV. Experimental and computational test methods are reviewed. Low Reynolds number aerodynamics are studied. The effects of airfoil aeroelasticity and geometry are discussed. Then, the application of the aerodynamics to flapping motions are reviewed. Finally, operational MAV designs are studied and recommendations are made to further advance the state of the art.