They served on the SS Madame de Pompadour and its sister ship, the SS Marie Antoinette. The former stalked Madame de Pompadour in 18th century France, believing that they could repair their ship by taking her brain. The former wore 18th century French clothing to blend in with the people of the era and were clockwork instead of electric so they could function if their ship's power was depleted.
The latter crashed in Earth's distant past and remained hidden until the Victorian era when their control node tried to repair the ship with both organic and mechanic material from Victorian London to take them to the "promised land". They disguised themselves using human skin taken from their deceased victims.
They followed camouflage procedures to blend into the surroundings. This could be as simple as dressing in appropriate costumes to match the time periods they found themselves in — despite looking somewhat unrealistic. (TV: The Girl in the Fireplace) A more drastic procedure of camouflage was the harvesting of human skin and organs to outwardly appear human. (TV: Deep Breath) They could be equipped with short range teleporters, scanners, tranquillisers and tools within their wrists for part removal. In the case of the Clockwork Droids aboard the SS Marie Antoinette, they were able to replace their tools with local spare parts, such as sword blades. They could also heat themselves if they were frozen and empty unwanted fluids from their system. Whenever they entered a room, they made "tick tock" noises from their clockwork parts. They broke any clock in the room to avoid raising suspicion. (WC: Tardisode 4, TV: The Girl in the Fireplace, Deep Breath)
The SS Madame de Pompadour Droids' only purpose was to fix the ship. When the ship was damaged in the Dagmar Cluster in an ion storm, they lacked the right parts. They used the crew members' body parts; according to the Tenth Doctor, "No-one told [them] the crew weren't on the menu." The last part they needed was a brain for their command circuit, and they believed that only the thirty-seven-year-old brain (the same age of their ship) of Madame de Pompadour would work. They modified the ship's warp engines to open many time windows to 18th century France and passed through it at various moments of Madame de Pompadour's life, attempting to find her in her thirty-seventh year. The Doctor defeated them by disconnecting the time window that led back to their ship. With no purpose, they shut down. (TV: The Girl in the Fireplace)
The SS Marie Antoinette crashed on Earth for at least 65 million years, due to their knowledge of dinosaur biology. Its robot crew managed to remain functional by constantly replacing the faulty parts with both organic and mechanic spares collected from their surroundings. These "spare parts" included dinosaur organs and Roman metalwork. However, as of the late 19th century, they changed their components so many times that almost nothing remained of the original androids. By that time, their ship had been reworked into a fake restaurant where unaware human victims were abducted and their organs harvested; the bodies were then burned to hide the missing parts. When the droids murdered a tyrannosaurus rex accidentally brought forward in time by the TARDIS for its optic nerve, the freshly-regenerated Twelfth Doctor found their base of operations and confronted their control node aboard the escape capsule of the ship — an enormous hot-air balloon made of human skin. The robots deactivated when the Half-Face Man fell to his death on the top of Big Ben. (TV: Deep Breath)
They were susceptible to multi grade anti-oil, which could stop them moving if it got into their circuits. Although, they could siphon it out. The Tenth Doctor used it on one, tricking it into believing it was wine by acting drunk. They could also be temporarily frozen. Their slicing device was also capable of becoming stuck in wood, something the Doctor used against them. (TV: The Girl in the Fireplace) Swords and energy weapons could also destroy them or at least disable them for a while. The Twelfth Doctor was capable of strong arming one if need be. Since the droids detected living beings by their breathing, they could be tricked into thinking that a living being was a droid too, by holding their breath. An example of this was Clara Oswald, who when trapped in the Clockwork droid's ship, held her breath for long enough to fool the droids and escape into a corridor before passing out from lack of air. (TV: Deep Breath) They lack common sense, as noted by the Doctor; they could have used the Spatio-temporal hyperlink to go the repair yard. However, they instead went after Madame de Pompadour, whose brain they thought they needed for the ship, as it was named after her. (TV: The Girl in the Fireplace)
Behind the scenes
The Clockwork Droids were based off the Turk, a clockwork man invented by Wolfgang von Kempelen of Vienna in 1770.