Ornithopters are vehicles that fly by flapping their wings, rather than trough use of a propeller or jet engine. They've been proposed and built many times throughout history, and are a common element of science fiction and fantasy.
Leonardo DaVinci's design for an ornithopter
There's at least one good reason why ornithopters have captivated so many: they are incredibly cool. However, while bio-mimicry can be useful for micro UAVs that are attempting to disguise themselves as birds, I'm not sure what advantages they would have over conventional aircraft. Is there any compelling reason, aside from a cool factor, why a civilization would develop and use ornithopters over fixed-wing aircraft?