Similarities and differences between the 2 main kinds of compound eye (apposition and superposition) are briefly explained before several promising topics for research on compound eyes are being introduced. Research on the embryology and molecular control of the development of the insect clear-zone eye with superposition optics is one of the suggestions, because almost all of the developmental work on insect eyes in the past has focused on eyes with apposition optics. Age- and habitat-related ultrastructural studies of the retinal organization are another suggestion and the deer cad Lipoptena cervi, which has an aerial phase during which it is winged followed by a several months long parasitic phase during which it is wingless, is mentioned as a candidate species. Sexual dimorphism expressing itself in many species as a difference in eye structure and function provides another promising field for compound eye researchers and so is a focus on compound eye miniaturization in very small insects, especially those that are aquatic and belong to species, in which clear-zone eyes are diagnostic or are tiny insects that are not aquatic, but belong to taxa like the Diptera for instance, in which open rather than closed rhabdoms are the rule. Structures like interommatidial hairs and glands as well as corneal microridges are yet another field that could yield interesting results and in the past has received insufficient consideration. Finally, the dearth of information on distance vision and depth perception is mentioned and a plea is made to examine the photic environment inside the foam shelters of spittle bugs, chrysales of pupae and other structures shielding insects and crustaceans.