Discovering that a shrimp can flick its eyes over to a fish and follow up by tracking it or flicking back to observe something else implies a 'primate-like' awareness of the immediate environment that we do not normally associate with crustaceans. For several reasons, stomatopods (mantis shrimp) do not fit the general mould of their subphylum, and here we add saccadic, acquisitional eye movements to their repertoire of unusual visual capabilities. Optically, their apposition compound eyes contain an area of heightened acuity, in some ways similar to the fovea of vertebrate eyes. Using rapid eye movements of up to several hundred degrees per second, objects of interest are placed under the scrutiny of this area. While other arthropod species, including insects and spiders, are known to possess and use acute zones in similar saccadic gaze relocations, stomatopods are the only crustacean known with such abilities. Differences among species exist, generally reflecting both the eye size and lifestyle of the animal, with the larger-eyed more sedentary species producing slower saccades than the smaller-eyed, more active species. Possessing the ability to rapidly look at and assess objects is ecologically important for mantis shrimps, as their lifestyle is, by any standards, fast, furious and deadly.