Hi.
As most animals, mantids use all the important senses. However, they may function different from that of verts.
1. Sight: well, no great secret: done by the compund eyes. There are zones of different sharpness, e.g. a foveal zone located in front.
2. Ocelli: these organs (3 simple eyes) are somewhat mysterious. It is presumed that they may help to orientate when flying, maybe they may percept different light frequencies. Males have always larger ocelli than females, and males are known to carry out nuptial flights. There exists a muscle which is attached to the ocelli, but nothing is known about the function.
3. Smelling, that is detecting chemical cues: done by the antennae. Often the food is slightly touched or the surroundings. Males and females can detect conspecific pheromones, important for mating. However, the loss of antennae does not alter food ingestion.
4. Tasting: located in the mouth, bad tasting prey is sometimes rejected, but hungry mantids usually "ignore" the taste.
5. Mechano- and thermoperception: receptors (trichosensilla and others) somewhat similar to the one on the antennae, located in the cuticula, usually spread over the body.
6. Hearing: the last discovered sense: located on the underside of the body between the coxae of the last leg pair (in some hymenopodids a second ear exists between the middle legs). As this ear of the tympamante type does not perceive direction it is called cyclopean ear. It is used for detecting bat sounds. It is developed well in all winged species, and better in males then in females. Mantids fly longer distances just by night, so this adaptation is quite useful. The ear is not able to distinguish the frequencies of its sensitivity range, so that may be the reason why there is a second ear in Hymenopodidae (other bats, other ears?).
Regards,
Christian