Dragonflies were some of the first insects to have evolve flight - the giant insect Meganeura, possessing a wingspan of 70-75 cm, was the size of some modern eagles with an appetite to match. It lived in the swamps of Western and Central Europe during the Carboniferous time period (around 311 MYA or so), and resembled a modern dragonfly in shape, behavior and development - its larvae lived in swamps, underwater, and ate various animals smaller than they were.
Meganeura was featured in both Walking with Monsters ep. 2 and Prehistoric Park ep. 5, both of which featured the Carboniferous, but by early Permian (Walking with Monsters ep. 2) the high oxygen content of the earlier Carboniferous time period had shrunk, and so had the insects - the dragonfly that briefly harassed the pair of Edaphosaurs is much smaller than the extinct Meganeura was.
Despite their dependency on water for their eggs and young, the dragonflies were among the survivors of the great Permian-Triassic extinction event, featured in Walking with Monsters ep.3: a Euparkeria is shown hunting them about 245-34 MYA, and later on in Walking with Dinosaurs ep. 1, several of the early pterosaurs also shown doing the same thing around 20 million years later. And in the following episode we see several other members of these insect species being hunted by Anurognathus - a small rhamphorhynchoid pterosaur.
Finally, the dragonflies have also survived the K/T extinction event: in Walking with Beasts ep. 1, an ancient mammal Leptictidium is shown hunting damselflies - a sister clade of the bigger dragonflies - 49 MYA, during the early Eocene time period.
Dragonflies and damselflies exist in modern times as well, even though water and air pollution has taken their toll on these insects.