When a young praying mantis leaps into the air, it can reach its target in literally a blink of an eye (less than a tenth of a second). Speed aside, the mechanics of a praying mantis jump is what makes it special: three different body parts rotate in different directions and different combinations in an incredibly skilled acrobatic act.
Once in the air the mantises precisely rotate three body parts -- the front legs, the hind legs, and the abdomen -- in different directions and in different combinations, all the time exchanging momentum between them and keeping the spin of the whole body at the correct rate to successfully reach and land on the target.
You can see them twist and turn in the video below. It's surprisingly graceful, even when they mistime their jump.