"Boneless" was the name the Twelfth Doctor gave to creatures from a two-dimensional universe. They were able to reduce both lifeforms and other three-dimensional objects to two-dimensional. After taking on three-dimensional forms themselves, they were also able to restore objects back from two-dimensional to three-dimensional. They also demonstrated the ability to drain dimensional energy from the Doctor's TARDIS, causing its external shell to be drastically reduced in size and weakened.
Biology
In their natural form, an individual Boneless manifested as a mass of transparent, writhing tendrils that could only travel across flat surfaces such as floors, walls or ceilings. In this form they had the ability to reduce a three dimensional object or person to two dimensions upon physical contact, literally flattening the target against whatever surface they were standing on. This process appeared extremely painful as one such victim, PC Forrest, screamed in agony when she was flattened. This process also resulted in the death of living targets, their corpses appearing as a mural flattened against a surface.
Their presence alone could leach dimensional energy from nearby sources such as the Doctor’s TARDIS, causing it to drastically reduce in size and eventually going into “siege mode” before completely losing all power.
The Boneless could dissect anything or anyone they had flattened in order to learn how its physical dimensions functioned. For instance, the only remains of one victim appeared as a microscopic blowup of human skin. Another “mural” seen was actually the human nervous system dissected from PC Forrest’s flattened corpse.
The skins or their dead victims could also be worn as “camouflage”, resulting in the Boneless appearing as warped versions of their deceased subjects.
Once they had learned enough, the Boneless gained the ability to transition from their natural two-dimensional forms to three dimensions. These forms were, however, imperfect, and constantly flickered between two dimensions and three dimensions, with parts of their bodies constantly deforming, reshaping, and disappearing and reappearing all the time.
The Boneless could also restore a flattened object to its normal three-dimensional shape by firing what appeared to be an orange electrical stream of energy from their hands onto the target. (TV: Flatline)
History
The Boneless experimented on and dissected three-dimensional lifeforms and objects, eventually learning how to exist as three-dimensional beings themselves. Their transformation into 3-D beings was not perfected however, resulting in an appearance where they seemed partially 3-D and partially 2-D.
Trapped in his TARDIS when its dimensions were drastically reduced, the Twelfth Doctor was assisted by Clara Oswald in investigating the cause of its miniaturisation. Upon discovering the creatures' presence, he initially hoped that their experimenting on the humans in Bristol was strictly due to some misunderstanding; the Boneless originated from a universe with only two dimensions, and therefore were unable to communicate in a language that 3-D organisms could comprehend. However, following some experimentation, he was able to establish rudimentary communication with them, consisting only of sonically encoded numbers. Their subsequent naming of the numbers on the jackets of both a previous victim and their next victim convinced the Doctor they were likely able to read, and were thus aware of what they were doing.
After the TARDIS was restored with the help of Clara and her newfound friend Rigsy, the Doctor, satisfied that he had given them a fair chance, used his sonic screwdriver and an energy field from the TARDIS to forcibly send them back to their home dimension. He did so without regard to their chances of survival on the return trip, and with the following warning to any more Boneless who wished to conquer his home universe: "You are not welcome here! This plane is protected! I am the Doctor!". The Doctor didn't know whether the Boneless entered his universe to invade, infiltrate or just to "replace" humanity, but he believed that the role they "seem[ed] determined to play" was that of "monsters", and with him being "the man that stops the monsters", it was his duty to defeat them. (TV: Flatline)
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The Doctor and Clara once again encountered the Boneless in London, where they were pulling people into comic books to send them into their realm. After the Doctor himself was trapped in a comic, he used the combined minds of all the trapped comic fans and a spatial and temporal flux in the TARDIS to free everybody, imploding the Boneless back to their dimension once again. (COMIC: The Fourth Wall)
References
As one of the aliens she had met during her travels with the Doctor, the Boneless were included in a series of notes written by Clara when she was planning to confess to Danny Pink via phone call about her continued adventures with the Doctor after previously telling him that she has ceased travelling with him. (TV: Dark Water)
After the Twelfth Doctor's mind was connected to a mind scythe, the "holiday snaps" the Doctor showed Kygon Brox included the Boneless. (COMIC: The Instruments of War)