In the last decade, the potential of Micro Aerial Vehicles (MAVs) has generated an enormous interest in this technology and numerous applications have therefore been proposed in military and civilian fields. More recently, researchers have begun to work on a new and miniaturized generation called Flapping Wing Nano Aerial Vehicles (FWNAVs) who could be particularly promising for the indoor inspection. Before to be able to use efficiently these FWNAVs, there are however significant scientific and technical challenges to solve due to the scaling down. These include aerodynamics of low Reynolds number flow, small-scale power generation and power storage, navigation and communication, propulsion and control as well as manufacturability. This paper sets out the potential applications of such FWNAVs and reviews some of the challenges related to aerodynamics, stability, and design trends.