One of the main bands of the so-called post-rock - label created in the 90s to define the complex and experimental music of groups such as Slint, Tortoise, among others, Mogwai was formed in the city of Glasgow, Scotland, by Stuart Braithwaite (guitar, vocals), Dominic Aitchison (bass, guitar), Martin Bulloch (drums) and John Cummings (guitar).

The group's first album was the compilation Ten Rapid, released in 1997, bringing together the band's first singles. On the first studio album, Young Team, Mogwai featured a temporary member, Brendan O'Hare, ex-Teenage Fanclub. On the following album, Come on Die Young, released in 1999, Barry Burns (keyboards, guitar) took the place left by Brendan O'Hare, officially becoming the fifth member of the band.

On the tour of the album Rock Action, released in 2001, the band passed through Brazil in May 2002, performing in São Paulo, Belo Horizonte and Rio de Janeiro.

Happy Songs for Happy People, an album with an ironic title, was released in 2003. Following that, Mr Beast came out in 2006. Later that year, Mogwai composed the soundtrack for the documentary "Zidane: A 21st Century Portrait", a film about French football player Zinedine Zidane.

In 2008, the band released the album The Hawk Is Howling. Two years later, the group's first live album, Special Moves, came out on CD/DVD.

After a long time having their albums released in the USA by Matador Records, in 2010 the band left that label and signed with Sub Pop. The following year, Hardcore Will Never Die, But You Will, Mogwai's seventh studio album, left. The band returned with a new studio album in January 2014, when they released Rave Tapes. In 2016,  Atomic came out, a soundtrack for the documentary "Atomic: Living in Dread and Promise". A new studio album arrived in 2017, under the name Every Country's Sun.

In 2021, the group released As the Love Continues. Mogwai's tenth album was received with acclaim by critics and fans.