Detecting motion is essential for animals to perform a wide variety of functions. In order to do so, animals could exploit motion cues, including both first-order cues—such as luminance correlation over time—and second-order cues, by correlating higher-order visual statistics. Since first-order motion cues are typically sufficient for motion detection, it is unclear why sensitivity to second-order motion has evolved in animals, including insects. Here, we investigate the role of second-order motion in prey capture by praying mantises. We show that prey detection uses second-order motion cues to detect figure motion. We further present a model of prey detection based on second-order motion sensitivity, resulting from a layer of position detectors feeding into a second layer of elementary-motion detectors. Mantis stereopsis, in contrast, does not require figure motion and is explained by a simpler model that uses only the first layer in both eyes. Second-order motion cues thus enable prey motion to be detected, even when perfectly matching the average background luminance and independent of the elementary motion of any parts of the prey. Subsequent to prey detection, processes such as stereopsis could work to determine the distance to the prey. We thus demonstrate how second-order motion mechanisms enable ecologically relevant behavior such as detecting camouflaged targets for other visual functions including stereopsis and target tracking.