"Boneless" was the name the Twelfth Doctor gave to two-dimensional beings from another 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.
History
The Boneless experimented on and dissected three-dimensional lifeforms and objects, and eventually learned how to exist as three-dimensional beings themselves. Their transformation into 3-D beings was not perfected however, resulting in an appearance that was a partial combination of 3-D and 2-D.
The Doctor had hoped that their experimenting on the humans in Bristol was strictly due to some misunderstanding; the Boneless originated from another dimension, and therefore may not have been able 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 conically encoded numbers. However their subsequent naming of the numbers on the jackets of both a previous victim and their next victim established that they could indeed read, and it was likely they were aware of what they were doing.
Satisfied that he had given them a fair chance, and that they could indeed understand him, the Doctor used his sonic screwdriver and an energy field from the TARDIS to forcibly send them back to their home dimension. He did so knowing that there was a chance many of them wouldn't survive the return trip, and gave a warning to any other Boneless who wished to conquer the 3-D universe: the Doctor would stop them. The Doctor didn't know whether the Boneless entered the 3-D universe to invade, to infiltrate, or to "replace" humanity, but he believed that the role they "seem[ed] determined to play" was that of "monsters". (TV: Flatline)
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 adventures with the Doctor. (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)
