Their debut album, Love in the 4th Dimension, was released on 6 April 2017, containing a number of singles previously released on their EP, The Road. The album was shortlisted for the prestigious Mercury Prize in 2017. The band is signed to Fiction Records and have toured internationally. They will be supporting Pixies on their 2019 UK and Ireland tour. The band gained exposure as they went in a co-headline tour in October 2015 with fellow London bands VANT and Inheaven.
Following that tour, they supported artists The Maccabees, Ezra Furman and The Vaccines. In 2016, the band signed to Fiction Records. In March, they release their debut EP, The Road. Later in March, 29 they released the single Cupid.
In August 2016, the group released a cover version of Madonna's Beautiful Stranger. On 16 December 2016, the band announced their debut album Love in the 4th Dimension, and released new lead single Formidable. They were play-listed by BBC Radio 1 in July 2016. The Big Moon played on Marika Hackman's second album, I'm Not Your Man, released in June 2017.