They stick off a large'ish bit of territory on which they hunt insects while flying back and forth. The male is blue, while the female has a green tail. See also mating, ditto, egg-laying, hunting male ...
This heron chicken caught a red dragonfly by the tip of the wing, but the dragonfly managed to escape as shown in the 2nd photo. I hope the wing has not been damaged! Photos of a less lucky frog. Click on photo to enlarge