Mantidflies look like the result of a mad scientist's experiment gone awry. It's as if Igor were sent to the spare parts bins, drunk, and returned with the wings of a dragonfly, the body of a paper wasp, the head of a damselfly, and the raptorial forelegs of a praying mantis. Then, the evil doctor welded them all together, and Voila! This is what we've got.
These insects have a lifecycle as bizarre as their appearance, and the hoops that they've got to jump through to make it to the adult stage may account for their seeming scarcity. I don't know of anyone who claims to see tons of mantidflies. There are only about four or five species in this part of the world, in about as many genera. Mantidflies are in the Order Neuroptera, along with lacewings, owlflies, antlions and that sort of thing. I believe this species is Dicromantispa interrupta.
Things only get weirder as one drills into the mantidfly lifecycle. A female carpet bombs the plants with clusters of hundreds of eggs. She needs to dump a lot of them, as the chances of an egg making it to the adult stage are slim indeed. After a few weeks, a tiny larval mantidfly pops out, and lurks in the foliage awaiting a suitable host. When an appropriate spider (other mantidflies use bees or beetles) comes along, the fledgling mantidfly leaps aboard and firmly attaches itself to the underside of the arachnid.
If all goes well, the spider eventually hauls her dangerous cargo to the nest. Should the larval mantidfly mistakenly board a male spider, it'll realize its error and attempt to cross over to the female when and if the male finds a partner and commences mating. The larva's relationship with the adult spider is phoretic: it is just using the spider to hitch a ride. If by some minor miracle the larval mantidfly makes it to the Holy Land - a spider nest - it will then hop off and ensconce itself with the arachnid eggs. There it will morph into a grublike form and feed on the spider's eggs, eventually pupating and transforming to the strange adult insect seen in these photos.