Their lineup includes Joe Newman (guitar/lead vocals), Thom Sonny Green (drums), Gus Unger-Hamilton (keyboards/vocals), and formerly Gwil Sainsbury (guitar/bass).

Their debut album An Awesome Wave was released in May 2012 in Europe, and in September 2012 in the United States, and won the 2012 British Mercury Prize.

[17] Alt-J (∆) were formed when Gwilym (Gwil) Sainsbury (guitar/bass), Joe Newman (guitar/lead vocals), Augustus (Gus) Unger-Hamilton[18] (keyboards/vocals) and Thomas Stuart (Thom Sonny) Green[18] (drums) met at University of Leeds in 2007.

[19] Unger-Hamilton (younger brother of Ferdy, head of A&R for Polydor Records) studied English, the other three Fine Art.

[21] The band's sound arose in part from living in student accommodation, where noise had to be kept to a minimum, as well as limited access to instruments.

[21][24] Their self-titled 4-track demo EP, ∆, was recorded with producer Charlie Andrew in London and featured the tracks "Breezeblocks", "Hand-Made", "Matilda", and "Tessellate".

[29] Andrew said that the band's sound was heavily influenced by unusual instrument choices, including drummer Thom Green's decision not to use cymbals.

[31] Alt-J supported Wild Beasts in April 2012 and played a minor headlining tour around the United Kingdom and Ireland in October of that year.

[32] The band have featured regularly on summer festivals, including Latitude, Bestival, Reading and Leeds, T in the Park, Green Man, Pukkelpop, and Lowlands.

[35] Besides the prize-money, the band saw an increase in their profile resulting in An Awesome Wave reaching number 13 on the UK Albums Chart.

On 3 March 2017 Alt-J began teasing their third studio album on their social media accounts with an audio clip captioned "00110011 01110111 01110111" (Binary code for "3ww").

[44] On 6 March 2017 Alt-J released "3WW", which features lead singer Ellie Rowsell of Wolf Alice, as a digital single and announced dates for the Relaxer Tour in support of the album.

[45] In anticipation of their third album, the band released an online video game,[46] whose soundtrack was their single "3WW,"[47] as well as announcing in May 2017 that they would be playing a five-date UK tour at seaside venues, starting on 4 September 2017.

"Fitzpleasure" was featured in the background of the 2015 film Sisters and in the main trailer for the video game Battleborn released in 2016.

[58] In 2016, their song "Left Hand Free" was featured in the Marvel Cinematic Universe film Captain America: Civil War.

The song describes the details of Capa's death ("A violent wrench grips mass / Rips light, tears limbs like rags") and imagines Taro's complementary emotions.

The visuals in a fan made music video by YouTube user David Dean Burkhart are taken from Godfrey Reggio's experimental film Powaqqatsi.