Detecting the direction of image motion is important for visual navigation, predator avoidance and prey capture, and thus essential for the survival of all animals that have eyes. However, the direction of motion is not explicitly represented at the level of the photoreceptors: it rather needs to be computed by subsequent neural circuits. The exact nature of this process represents a classic example of neural computation and has been a longstanding question in the field. Our results obtained in the fruit fly Drosophila demonstrate that the local direction of motion is computed in two parallel ON and OFF pathways. Within each pathway, a retinotopic array of four direction-selective T4 (ON) and T5 (OFF) cells represents the four Cartesian components of local motion vectors (leftward, rightward, upward, downward). Since none of the presynaptic neurons is directionally selective, direction selectivity first emerges within T4 and T5 cells. Our present research focuses on the cellular and biophysical mechanisms by which the direction of image motion is computed in these neurons.