Selected data from optics, histology, electrophysiology and behavior in vision of mantis shrimps are summarized. These data lead to models for three parallel systems in visual processing: for a location and an image analysis system and for figure-ground discrimination. The location and the figure-ground systems are based on single neurons. The image analysis relies on spatio-temporal activity patterns distributed over the first visual ganglion. The patterns can be interpreted and classified by neural networks. Interaction of the different systems, of these with action neurons or networks and of the nervous correlates for the three subsystems are still speculative.