Flying wing aircraft predate the First World War. The flying wing theoretically offers both aerodynamic efficiency and structural simplicity. Early efforts to develop the flying wing concept led to an increased interest in tailless and semi-tailless aircraft that eventually led to delta wings and swept wing planforms. Early flying wings were plagued by stability and control problems that have not been fully addressed until recently. The flying wing approach, however, still appears to be suitable only for aircraft that do not need to have high maneuverability and agility capabilities, such as long-range bombers or perhaps large transports. This paper surveys the long history of attempts to create flying wing aircraft.