Human eyes have a widely exposed white sclera surrounding the darker coloured iris, making it easy to discern the direction in which they are looking1. We compared the external morphology of primate eyes in nearly half of all primate species, and show that this feature is uniquely human. Humans have the largest ratio of exposed sclera in the eye outline, which itself is elongated horizontally. We suggest that these are adaptations to extend the visual field by allowing greater eye movement, especially in the horizontal direction, and to enhance the ease of detecting the gaze direction of another individual.