Micro Aerial Vehicles (MAVs) are increasingly regarded as a valid low-cost alternative to UAVs and ground robots in surveillance missions and a number of other civil and military applications. Research on autonomous MAVs is still in its infancy and has focused almost exclusively on integrating control and computer vision techniques to achieve reliable autonomous flight. In this paper, we describe our approach to using automated planning in order to elicit high-level intelligent behaviour from autonomous MAVs engaged in surveillance applications. Planning offers effective tools to handle the unique challenges faced by MAVs that relate to their fast and unstable dynamics as well as their low endurance and small payload capabilities. We demonstrate our approach by focusing on the "Parrot AR.Drone2.0" quadcopter and Search-and-Tracking missions, which involve searching for a mobile target and tracking it after it is found.