Order of the Headless

The Headless Monks were a religious order who believed in listening to their hearts rather then their minds, to the point of having themselves beheaded.

Biology
As they were headless they did not register as living beings. The monks were also supposedly incapable of being fooled. Despite their lack of heads they seemed to be able to see fine, or at least were able to detect where other beings were. They could also fire energy out of their hands.

They could also be killed as easy as most other humanoids, with energy or sword wounds.

Technology
They were armed with swords that gave off some sort of orange energy, although they could be deflected with ordinary swords.

History
The Headless Monks were present at Demons Run when they fought the Eleventh Doctor and his allies. (DW: A Good Man Goes to War) The Delirium Archive was said to be their final resting place. (DW: The Time of Angels)

Behind the scenes

 * The Monks resemble the unnamed cowled figures from TW: Exit Wounds.