The band started when Harriet Wheeler and guitarist David Gavurin met.
The Sundays got a record deal with the Rough Trade Records. Their first single, "Can't be Sure", was released in 1989. Their first album, Reading, Writing and Arithmetic, was released in 1990. The album got very positive reviews. It entered the UK chart at #4. Later in 1990, the album peaked at #39 in the United States. Its success came mostly from radio stations playing "Here's Where the Story Ends".
In late October 1992, the next album, Blind, was released. This album was also successful when it peaked at #103 on the Billboard 200. Blind sold half a million copies. The reviews were positive. Some critics thought the album didn't have the quality songwriting of the first album.
In autumn 1997, after five years, their third record, Static & Silence, was released. It got mixed reviews. "Summertime", the first song on the album, was their most successful song the UK Charts up to that time.
The Sundays took a break after the album Static & Silence.