Nanotechnology was the manipulation of matter on an atomic and molecular scale. They usually took the form of microscopic robots, often referred to as nanobots or microbots. Many species had developed nanotechnology.
Medical nanomachines on the human colony planet Rua were protein-based and inorganic machines which could target infection, rewrite DNA, and encourage repair of cartilage, tissue, and bone. (AUDIO: The Sleeping Blood)
After being stranded in the past, Ramón Salamander improved on his weather creating technology by creating the micro machines, infinitely combining nanites that could makeshift themselves into any construct and assimilate any raw materials as fuel. (COMIC: The Heralds of Destruction)
By other species
Gallifrey developed nanomedicine thousands of years before Susan's time, and she could easily manipulate the nanomachinery she found on Rua, thanks to her experience with them on her home planet. (AUDIO: The Sleeping Blood) When trapped inside his TARDIS, the Twelfth Doctor provided Clara Oswald with a nanotech earpiece that allowed him to see through her eyes as she investigated the Boneless. (TV: Flatline)
The Daleks' network of ionising towers incorporated nano-particles into each burst of static electricity to guide the bursts to their targets. (AUDIO: Return to Skaro) The Daleks later created the Contagium, which could infect biological hosts with nanites, allowing the Daleks to control their minds. (COMIC: Fire and Brimstone) They later created nanoclouds which converted organic matter into Dalek puppets. (TV: Asylum of the Daleks)
The Actilliasauraitius Mining Corporation used nanobots to set up a mine on the planet Adamantine. The Thirteenth Doctor later reprogrammed the nanobots to seal up the mine, thereby saving the rock people living inside the planet from destruction. (PROSE: Molten Heart)
In an alternate timeline created when Rassilon joined forces with the Cyberiad, the Cybermen created the techno-virus, a nanite swarm that was capable of rapid conversions on a planetary scale. (COMIC: Supremacy of the Cybermen)