How neurons detect the direction of motion is a prime example of neural computation: Motion vision is found in the visual systems of virtually all sighted animals, it is important for survival, and it requires interesting computations with well-defined linear and nonlinear processing steps—yet the whole process is of moderate complexity. The genetic methods available in the fruit fly Drosophila and the charting of a connectome of its visual system have led to rapid progress and unprecedented detail in our understanding of how neurons compute the direction of motion in this organism. The picture that emerged incorporates not only the identity, morphology, and synaptic connectivity of each neuron involved but also its neurotransmitters, its receptors, and their subcellular localization. Together with the neurons’ membrane potential responses to visual stimulation, this information provides the basis for a biophysically realistic model of the circuit that computes the direction of visual motion.