Research over the past century has revealed the impressive capacities of the honeybee, Apis mellifera, in relation to visual perception, flight guidance, navigation, and learning and memory. These observations, coupled with the relative ease with which these creatures can be trained, and the relative simplicity of their nervous systems, have made honeybees an attractive model in which to pursue general principles of sensorimotor function in a variety of contexts, many of which pertain not just to honeybees, but several other animal species, including humans. This review begins by describing the principles of visual guidance that underlie perception of the world in three dimensions, obstacle avoidance, control of flight speed, and orchestrating smooth landings. We then consider how navigation over long distances is accomplished, with particular reference to how bees use information from the celestial compass to determine their flight bearing, and information from the movement of the environment in their eyes to gauge how far they have flown. Finally, we illustrate how some of the principles gleaned from these studies are now being used to design novel, biologically inspired algorithms for the guidance of unmanned aerial vehicles.