Of Irish-Italian parentage, Elena Tonra (b. 1990) was raised in Northwood, London, with her older brother, Kieran. Through her Dublin-born grandfather she experienced traditional Irish music from an early age. Her interest in music began when she received a copy of the album Grace by Jeff Buckley. After being bullied at school she used writing to "deal emotionally with life". Changing schools at the age of 12 had a great impact and since then Tonra writes "about things I feel difficult talking about in adulthood”.
Tonra began her career in music, performing acoustic shows under her own name around London, she found that this "didn’t suit me at all. As a musician, I’m self-taught and felt I was restricted by my abilities". Haefeli attended one of the acoustic shows that Tonra was performing and found that "she had this power which drew everyone in". Originally from Neuchatel, Haefeli also attended London's Institute of Contemporary Music Performance where he met Tonra during a songwriting course. They began performing together with Haefeli adding electric guitars. After their first demo started word of mouth on the band, Daughter self-released their debut EP, His Young Heart, on 20 April 2011, recorded in Haefeli's bedsit. Later that same year, they released another EP, The Wild Youth, on 2 October through artist-led Communion Records. The latter EP earned praise from British website For Folk's Sake who described Daughter as "one of the unique sounds in the pop landscape today." BBC Radio 1 DJ Huw Stephens also invited them to perform a Maida Vale Session for his show.
Tonra and Haefeli became romantically involved and the guitarist insisted that they "keep our couple life and our band life separate, [because] I don’t want Elena to stop saying things in her songs that are personal [as] songwriters need to be expansive and they need to be unafraid”. While Tonra concurred with "Igor doesn’t question my lyrics. He regards what we do as an art form. He certainly doesn’t try to rewrite my words. I never tell anyone what my songs are about, not even him. I feel they are direct enough, anyway. They aren’t especially obscure".
In 2012, shortly after headlining a 700-capacity show in London, Daughter announce their signing to UK label 4AD. Speaking of this, Elena commented "we couldn't be happier to be working with 4AD, a label that has released so many inspirational records and whose ethos we hold in very high regard. It really is a privilege." Their first single proper, "Smother", was released in October of that year. It was playlisted by both BBC Radio 1 and 6Music, while being awarded Single of the Week by long-time supporter Huw Stephens. In December 2012 the band appeared on the David Letterman Show prior to the release of the record, which Tonra described as "perhaps (...) a cart-before-the-horse situation".
The band released their debut album, If You Leave, in March 2013 (May in Norway). Charting at Number 16 in the UK, it was also received favourably in the press; "An album as beautifully conceived as If You Leave is one you follow from start to finish, riveted by the story it weaves and the emotion it bleeds. And in these digital days that feels like a remarkable achievement" Drowned in Sound said in their 9/10 review, while The Fly in a 4/5 album review said that it's "word-in-the-ear intimate and mountain-range massive". Daughter also won Independent Album of the Year for If You Leave at the 2013 AIM Independent Music Awards in London. The band began a lengthy tour in support of the album and recruited Luke Saunders as an additional live-member to ensure the material could be reproduced. As Haefeli explained: "He plays everything we can’t play, which is keyboards, bass and some more guitar. We were really happy with the result. It took quite a while and a lot of rehearsing, but we are really happy with how the songs sound live". The band also use a number of vocal and guitar effects to achieve this sound live.
During the first two months of 2014, the band travelled to the Far East and Australasia for a number of headlining shows and as part of the St Jerome's Laneway Festival. In April, Daughter supported The National on six North American tour dates, while they also announced the release of a 4AD Sessions EP, a collaboration with composer Joe Duddell. It consists of five tracks performed live at Portmeirion with an eight-piece ensemble that was also filmed.
In September 2014, the band indicated that they had started working on a follow-up at their own studio in London. Haefeli explained: "We've played so many shows that the first album became rockier on stage and we're playing with that dynamic". On April 6th, 2015, Daughter announced they would be supporting Ben Howard on a short string of tour dates in the United States.
On 30 September the band announced that they would release the 10-track album Not To Disappear in January 2016 while the first single, "Doing The Right Thing", was made available.