H is for... Harmony Shoal

A parasitical race of brain-like creatures, which planned to take over the Earth. Their intention was to have themselves transplanted into the heads of the world's most powerful and influential figures. They infiltrated a global company - Harmony Shoal - which had constructed headquarters buildings in most of the Earth's major cities. A derelict spacecraft was in a hidden orbit, programmed to crash onto the city of New York. The Harmony Shoal building was built especially to withstand such a catastrophe, whilst the rest of the city would be destroyed. The plan was that all the leading figures in each country - politicians, businessmen and military leaders - would observe this and take refuge in other Harmony Shoal buildings, in fear of further attacks from space. There, they would have their brains removed and replaced by the aliens.

Those already taken over exhibited a livid scar running diagonally across the face, and they sometimes bled a blue fluid which was secreted by the creatures. The head could be opened along this scar-line.
The Doctor and his companion Nardole were investigating the New York operation, when they encountered an investigative journalist named Lucy, who was similarly suspicious of the company and its boss, Mr Brock, who had been converted by his colleague Dr Sim. They were rescued from Sim by the arrival of the city's masked superhero, known only as The Ghost. Brock and Sim became determined to capture the Ghost so that one of their number could be transplanted into his body.
The Doctor scuppered their plans by crashing the spaceship prematurely - knowing that the Ghost would save the city. UNIT were then called upon to raid all Harmony Shoal buildings across the planet. The Sim alien escaped, however, by transferring into the body of a UNIT soldier.

The Doctor had met this species before, in the far future, when he and River Song had rendezvoused with potential buyers for a fabulous diamond on the spaceship Harmony and Redemption. River had stolen this diamond whilst it was still embedded in the skull of her latest husband - the cyborg King Hydroflax - by removing his head from his robotic body. What the Doctor and River didn't realise was that the buyer - a man named Scratch - was a member of the Shoal of the Winter Harmony, a branch of the same parasitical aliens, and they worshipped Hydroflax like a god. All of the guests at the restaurant where the exchange was to take place exhibited the same diagonal scarring. The Doctor and River only escaped by deliberately crashing the spaceship onto the surface of the planet of Darillium - killing all on board, including the members of the Shoal.

Played by: Robert Curtis (Scratch), Tomiwa Edun (Brock) and Aleksandar Jovanovic (Sim). Appearances: The Husbands of River Song (2015), The Return of Doctor Mysterio (2016).

• Moffat elected to bring back these aliens in their own story for the 2016 Christmas Special, following their brief appearance towards the end of the previous year's festive special as he felt they had the potential to carry a story on their own, where he could develop them further.
• The second appearance has Brock simply disappear, and Sim escape in a different body, so the option was there for further appearances.
• The question has to be asked: if the creatures have to be transplanted into other people's heads by someone else, how was the first one created?