The Weave were a race made of wool.
They were all one giant family and had numbers instead of names. They had the ability to weave into different objects, including all of their technology and ships. They also had the ability to take the form of other people, providing they had a live template.
The Eleventh Doctor recalled meeting them when he saved their home planet "about five or eight faces back...". He made friends with one of them, she was seven or eight and welcomed him to a dinner with her family as thanks. As a reward for saving their planet they offered him the Glamour, a drug-type substance that changed reality to give the user pleasure. The Tahnn were at war with the Weave because they wanted to use it as a weapon. The Doctor took the girl for a ride in the TARDIS and then he gave her a device to call him for help.
When the Doctor, Rory and Amy landed on Earth in 1936, the Weave were hiding, by taking the form of humans, from the Tahnn. Rory was the first to find they were on the planet. He met a "librarian". She went to make him a cup of tea. A few minutes later, he went into her room and saw her face in a hammock/pod type object made out of a horrible green wool. Rory told the Doctor and the Doctor told them about the Weave and that they were at war with the Tahnn. (PROSE: The Glamour Chase)