Previous work has suggested that dragonfly ocelli are specifically adapted to resolve horizontally extended features of the world, such as the horizon. We investigate the optical and anatomical properties of the median ocellus of Hemicordulia tau and Aeshna mixta to determine the extent to which the findings support this conclusion. Dragonfly median ocelli are shown to possess a number of remarkable properties: astigmatism arising from the elliptical shape of the lens is cancelled by the bilobed shape of the inner lens surface, interference microscopy reveals complex gradients of refractive index within the lens, the morphology of the retina results in zones of high acuity, and the eye has an exceedingly high sensitivity for a diurnal terrestrial invertebrate. It is concluded that dragonfly ocelli employ a number of simple, yet elegant, anatomical and optical strategies to ensure high sensitivity, fast transduction speed, wide fields of views and a modicum of spatial resolving power.