Abstract: Flies represent nearly 10% of all species described by science and are arguably unmatched among flying organisms in their aerial agility. The flight trajectory of flies often consists of straight flight segments interspersed with rapid changes in course called body saccades. Flies’ ability of generate these precise maneuvers is due in part to a remarkable wing hinge that is equipped with specialized flight control muscles, as well as elaborate equilibrium organs called halteres that function as gyroscopes. Recent advances in genetic tools have made it possible to explore the neurobiological circuitry underlying the flight behavior of flies. Whereas the rapid turns are controlled by just a small set of descending command interneurons, the animals’ ability to fly straight relies on a much larger number of descending neurons that work via a population code to sustain the large, yet precise, bilateral differences in wing motion that are required to compensate for either wing damage or asymmetries generated during development. Whether regulating straight flight or generating rapid turns, the commands from descending neurons are executed via a small population of tiny steering muscles that echo the functional stratification of the upstream circuitry. One behavior that is responsible for the remarkable ecological diversity of dipteran insects is their uncanny ability to track attractive odor plumes to their source. In this lecture, I will argue that flies’ virtuosic power of odor localization results from their ability to estimate wind direction each time they execute a body saccade—a feat they accomplish using a specialized region of their brain to perform vector computations.