Is that a toy someone dropped?
No, it's a Tinkertoy or something.
Wait--it's a tiny alien, and now I'm freaked out.
Oh, it's a praying mantis. And I'm still freaked out.
There's something unnerving, unnatural, and intelligent about the way the mantids move around that makes a lot of people instantly wary. Their articulating legs, their hypnotic, swaying motion, and the freaky way their heads track you as you walk around them, working up the courage to shoo it away.
As predators of other arthropods, they are beneficial, in that some of the insects they eat probably would have harmed your vegetation. However, a lot of the other ones they eat would have helped your vegetation, so there's debate about how much good they actually do in your yard. They don't focus on a single type of prey, so they end up eating the good with the bad insects. But even though they are freaky, we don't go out of our way to kill this insect.
After a few seconds of sizing up its prey, the grasshopper pounced on the mantis, defeated it, and began eating. This is not what we expected at all, but we were still excited to have seen something gross.
So they're not undefeatable! And they're not actually all that ornery, although you can rile them up by poking them with grass, getting too close to their strange heads, or by insulting their mothers.
But if you happen to find one on your leg, like I did last night, you may at first think it's a shoelace. But when kicking your ankle sideways doesn't cause it to fall away, and you look down and see two large eyes looking back at you, you needn't freak out. Just scrape him off onto the nearest bush, and congratulate yourself for being so brave. And the longer it takes your camera to focus at that distance, the braver you are.