Some invertebrates have complex eyes that provide novel insights beyond what has been discovered about visual processing in the vertebrate eye. One group of crustaceans called stomatopods, or mantis shrimp, have large compound eyes, and social and predatory behaviors that depend on sophisticated visual processing of form, motion, and color. The eye contains three bands of facets providing overlapping fields of view that may aid in directing the predatory strike. Some species' eyes have ten or more visual channels for spectral sensitivity and polarized light detection. These animals include a diversity of species occupying tropical marine habitats; some occupy coastal areas where color vision in daylight is practical, while others are in deeper or murkier water, or are nocturnal. Each species has its own pattern of body coloration, ocular anatomy and retinal physiology. This work will examine the visual system in the context of the behaving animals in their environment, to try to extract how these visual systems are optimized for high performance. Techniques of spectrophotometry, histology, chromatography, radiometry, and ethology will be used to characterize visual pigments, intraocular filters, body coloration, photic environments, and the ability of the animals to discriminate hues. Results should clarify how stomatopod vision is specialized for behavior in diverse habitats. This unusually multifaceted approach on the mechanisms of a well-defined biological system in its environment should have impact on visual science, sensory neurobiology, ethology, and zoology, and might be very interesting to workers on machine vision.