When Wonder Woman was able to return Steve Trevor back to Man’s World, she was given an invisible plane designed by Amazon science to take him in. Even though the plane was invisible, the occupants of the plane, including the pilot do not also gain invisibility. In the 1940s, it was to be called the “Transparent Plane”. Within the comics, it was a piece of Amazonian technology, as the Amazons were depicted with advanced technology. The plane was originally hidden in an abandoned farm, and Wonder Woman’s telepathic powers from her tiara gave her control of the plane and that she could call for the plane at the speeds of sound. The plane also had a drop ladder which was also invisible, and she was usually drawn sitting on the plane wing, controlling the plane from there and battling airborne villains. During the Golden Age in comics, continuity was not important and the invisible plane had another origin story. With this one, she was to do three tasks, and if she completed in the three tasks, her reward would be a part of the plane, and then she would be able to form the plane with the three parts.
During the Silver Age, a new origin story was created. She was to tame a horse called Pegasus and if she could, Pegasus would become the invisible plane would through the other end of the mystic clouds that separated Man’s World and Paradise Island. The plane then became a jet as new technology was being invented and the plane this time could travel in outer space and allowed many of her friends to also ride along. The rope was rarely used this time however, as Wonder Woman could just pounce up onto the plane and use air currents to glide her towards the jet. The jet is destructible however as Wonder Woman is blinded and ends up crashing the jet near Gorilla City.
During this time, the jet’s origin story was revised and it was rarely used as Wonder Woman now had the ability to fly. Its origin was that Wonder Woman had been given a Lansinar disc which was a “morphing crystal”. This technology was devised as the aliens who created this were blind and could not adapt to their environments quickly enough and so this the crystal was created, so that it could morph catering to their needs. This time, the jet was invisible, and it made the occupants inside invisible as well and propels itself using graviton particles. This jet could also go into outer space and without taking a deep breath; Wonder Woman could stay in space for 20 minutes using the jet’s oxygen supply. It could also attune to her needs telepathically. The jet has weapons, but is rarely used as this depletes the jet’s resources and can render the plane visible. Though it can regenerate, it does it slowly and it is used as a last resort. The jet was still used because it could hold many people, even though Wonder Woman could fly.
Established in issue #140 that the Invisible Plane can shape itself into a flying fortress known as the WonderDome. This WonderDome would serve as Wonder Woman's equivalence to Superman's Fortress of Solitude and Batman's Batcave although she has areas more pertinent to her upbringing such as a sculpture garden.
New 52: Post -Flashpoint
In 2011, DC Comics rebooted their entire comic universe. In this new continuity, the Invisible Plane never belonged to Wonder Woman. Instead, it was designed by the Homeland Security offshoot organization, A.R.G.U.S., and serves as the main form of transportation for Amanda Waller & Steve Trevor's "Justice League of America".