Dragonflies are ancient: with damsel flies, they were among the earliest flying insects. An analysis based on molecular data and fossil evidence suggests a date of 480mya for the first insects, around the same time that land plants evolved, and includes a rather impressive family tree for the taxon; the earliest dragonfly fossils are around 325my old.
Back when I was doing my Hons year at uni, a friend was studying feeding in nymphal dragonflies, which was quite something to watch! (The feeding, not the friend.) If you look at them head-on – there's a good view in this video – they've got a well-developed set of mandibles. But the thing to watch out for, if you're something dinner-sized, is the big, extensible labium (analogous to a lower jaw) – this shoots out at great speed to catch passing water boatmen, mosquito larvae, or other suitable prey.
So, they're active predators, and this means that they need excellent vision. Like all insects, dragonfly eyes are based on units called ommatidia. However, dragonfly eyes are huge. Most of the animal's head is covered by the two compound eyes, each of which is made up of roughly 28,000 of those ommatidia. Much of their brain must be given over to processing that information, given the speed at which they move and the accuracy of their attacks (apparently up to 95% of attempts on prey are successful).
And since I mentioned speed, here's a video from the BBC on just how quickly dragonflies react to the sight of potential prey.