I think much of the long-standing conventional wisdom was that the tails mostly serve as camouflage of sorts, to help a moth perched among plant matter better blend with its surroundings. At least that's what I always thought. The tails undoubtedly do serve that role, too. I've seen Lunas hanging among green leaves on occasion, and the streamers do seem to break up its shape.
But there seems to be a more critical role for the tails...
I am about sure that's what happened to the moth in the photo above - a survivor of a failed bat attack. The V-shaped bite mark on the wing, especially, is the calling card of a bat.
My whole life has been moths for a while, because of a book project, and it has me frequently dipping into the files and dredging up old photographic chestnuts such as these moths.