The name Cocteau Twins was chosen in honor of the song with the same name by a group called Johnny and the Self-Abusers (later they will change their name to Simple Minds, and the same song was renamed 'No Cure').

In 1980, in a discotheque in Grangemouth (Scotland) called 'Nash', Robin Guthrie and Will Heggie met Elizabeth Fraser, who they chose as a singer for their band, Cocteau Twins.

The first album of the Cocteau Twins, 'Garlands', was published in 1982, it's still close enough to Goth music and however it gained a good success. A few months after their debut album, the Cocteau Twins published the ep 'Lullabies', founding the 'dream pop', the genre that made them famous.