Picture by Tom Sullivan, taken from S.Petersen's Field Guide to the Cthulhu Mythos.
[The flying polyps were a] horrible elder race of half polypous, utterly alien entities... They were only partly material and had the power of aerial motion, despite the absence of wings... [They exhibited] a monstrous plasticity and ... temporary lapses of visibility... [S]ingular whistling noises and colossal footprints made up of five circular toe marks seemed also to be associated with them.
—H.P. Lovecraft, "The Shadow Out of Time"
The flying polyps came to Earth out of space as conquerors about seven hundred and fifty million years ago. They also inhabited three other planets in the solar system, including possibly Yaksh (Neptune) and Tond (though Tond itself may lie outside the solar system). S. T. Joshi suggests that one of the mysterious solar planets inhabited by the polyps might have been Yuggoth (Pluto) because its windowless buildings "would be admirably suited to these sightless denizens!" (Joshi, "Lovecraft's Other Planets", p. 36, Selected Papers on Lovecraft.) On Earth, they built basalt cities with high windowless towers in what is now Australia. When they attempted to colonize the oceans, the polyps were driven back by the Elder Things. Thereafter, they restricted their habitats to the surface world.
Their senses did not include sight, but what senses they had could penetrate all material obstructions. They were only partially matter, but still solid enough to affect and be stopped by normal materials; this additionally gave them resistance, if not outright invulnerability, to normal means of damage, though they could be destroyed by certain forms of electrical energy. They are able to levitate and fly despite lacking any visible means of doing so, and leave telltale massive footprints when on the ground. Their amorphous bodies can turn invisible at will, though this ability appears somewhat negated by whistling noises associated with them in general. In battle, their ability to control and direct powerful winds is put to use as a weapon.
When the Great Race of Yith came to Earth, they warred with the polyps and soon drove them underground with their advanced technology. The Great Race then sealed the entryways to the polyps' subterranean abode with trapdoors, which afterwards were diligently guarded. The polyps' cities were left abandoned, perhaps as a reminder of the horrors that dwelt below.
Eventually, the polyps rose up and exterminated the Great Race, afterwards returning to their subterranean haunts. Having no conception of light, the polyps seem content to remain there, annihilating the few intruders that chance upon them. The entrances to their dwellings are mostly deep within ancient ruins where there are great wells sealed over with stone. Inside these wells still dwell the polyps.
Source: H.P. Lovecraft's short story "The Shadow out of Time". , (1982), The Best of H.P. Lovecraft: Bloodcurdling Tales of Horror and the Macabre, 1st ed., Ballantine Books. ISBN 0-345-35080-4., Harms, Daniel (1998). “Flying Polyps”, The Encyclopedia Cthulhiana, 2nd ed., Oakland, CA: Chaosium, p. 109. ISBN 1-56882-119-0, Joshi, S. T. (1989). “Lovecraft's Other Planets”, Selected Papers on Lovecraft, 1st printing, West Warwick, RI: Necronomicon Press. ISBN 0-940884-23-2.