Order of the Headless
The Order of the Headless, commonly known as the Headless Monks, were a religious order who believed in listening to their hearts rather than their minds, to the point of having themselves beheaded.
Biology
As they were headless, the Headless Monks did not register as living beings. They were also supposedly incapable of being fooled or feeling fear. Despite their lack of heads, the Monks were able to detect where other beings were. They could also fire energy blasts from their hands, as well as channelling that energy into the swords they carried.
They could be killed just as easily as most other humanoids, with energy blasts, guns, or sword wounds. They also had some form of vocal ability, as they could chant. (DW: A Good Man Goes to War)
Culture
The Headless Monks were very religious. They believed in listening to their hearts rather than their minds, so they beheaded themselves, and placed their heads inside an unnamed, box-like device. If another group allied with the monks, they were expected to provide at least one of their members to join the monks.
It was a Level One Heresy, punishable by death, to attempt to lower the hood of a Headless Monk. The group followed an entity known as the Papal Mainframe. Although the monks considered it a heresy to reveal their headless state to outsiders, they were apparently able to do so under the orders of the Mainframe.
The Monks would perform an attack chant before certain fights. (DW: A Good Man Goes to War)
History
The Order of the Headless joined an alliance, along with the Anglican Regiment of The Church and Madame Kovarian, dedicated to the defeat of the Doctor. Some time after Amy Pond's honeymoon, after her child was conceived, she was captured and replaced by a Ganger perfectly synced to the real Amy so that neither the Doctor nor Rory Williams, Amy's husband, would notice.
As far as Amy knew, she was continuing her adventures with the Doctor and Rory. In reality, Amy's pregnant body was taken to Demons Run in the 52nd century. The Headless Monks went to great effort to contain her and her unborn child. (DW: A Good Man Goes to War) They paid Dorium Maldovar for delivering them the brain of a Judoon trooper, which contained security software they needed. (WC: Prequel (A Good Man Goes to War))
In accordance with the Headless Monks' alliance protocol, one Cleric was to be initiated into their religion. Later, during a speech by Colonel Manton, he was allowed to unveil the monks to reveal knots of skin where the bases of their necks should be. The third monk removed his own hood, revealing himself to be the Doctor in disguise. When the lights were turned off he vanished and claimed he was one of the monks. A marine shot a hooded figure who turned out to be a real Monk. The Monks began to kill the marines in retaliation until the Colonel told everyone to ceasefire. With the Monks and Clerics unarmed, the Doctor's own forces, an army of Silurians and Judoon led by Sontaran Commander Strax, suddenly appeared.
Colonel Manton was forced to surrender and he, Kovarian and the rest of the Clerics (bar Lorna Bucket) abandoned the base. However, the Headless Monks struck, massacring most of the Silurians before they even noticed. The Monks then surrounded the Doctor's remaining allies, Rory, Dorium, Strax, Madame Vastra, Jenny and Lorna. After converting Dorium into a Monk, a battle started. This resulted in all the Monks being killed, while Strax and Lorna were both mortally wounded and died shortly afterwards. (DW: A Good Man Goes to War)
In 171st century, the Delirium Archive was said to be the final resting place of the Headless Monks. (DW: The Time of Angels)
