"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.
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)
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)
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)