Helicopters have the potential to transform Mars exploration by providing a highly mobile platform for forward reconnaissance as an aid for ground-based systems. NASA is therefore considering the possibility of sending a small helicopter to the Martian surface as part of a future mission. Helicopter flight on Mars is challenging due to the extremely thin atmosphere, which is only partially offset by a reduction in gravity. In this paper we focus on flight dynamics and controllability issues for the proposed Mars Helicopter, in particular the areas in which the dynamics departs from typical behavior on Earth. We discuss insights gained from modeling and simulation as well as system identification performed with a test vehicle in the relevant atmospheric condition, which culminated in the first demonstration of controlled helicopter flight in Martian atmospheric conditions in May 2016.