As they grew older, the girls became more interested in incorporating pop and contemporary R&B into their music. In 2006 they decided to form their own band. For the next five years, Haim played local venues, but did not take things further as all three sisters were busy with other projects. Este was studying at UCLA and graduated in 2010 with a degree in Ethnomusicology, completed in just two years instead of the normal five. Upon graduating from high school Danielle was asked to play drums for the opening act on one of Jenny Lewis's tours, which led to Lewis asking Danielle to be her guitarist on the following tour. The Strokes' singer Julian Casablancas came to see one of Lewis's shows on that tour, and he in turn asked Danielle to play guitar and percussion on his own solo tour. She has also toured as part of Scarlet Fever, the all-female backing band for CeeLo Green. It was after Danielle had played with other artists and Este had graduated that the sisters decided that they wanted pursue their career as Haim more seriously. Youngest sister Alana spent one year in college before dropping out to join the band with her sisters.
Having played shows supporting artists such as Edward Sharpe and the Magnetic Zeros, The Henry Clay People and Kesha, Haim's first release was a three song EP titled Forever which was made available on February 10, 2012 as a free download on their website for a brief period. The EP received a lot of attention from the music press and the general public, and following a successful gig at the South by South West festival in March 2012 Haim signed a deal with Polydor Records in the UK in June 2012. In July 2012 independent record label National Anthem released the Forever EP on 10" vinyl, containing the original three songs along with a fourth track, a remix of "Forever" by Dan Lissvik. All songs on the Forever EP were included on Days Are Gone, except for "Better Off".  Following dates supporting Mumford & Sons on their "Gentlemen of the Road" tour in the US in August 2012, Haim made their debut tour of the UK in November 2012 and then supported Florence and the Machine on their UK and Ireland tour in December 2012.
"Forever" was released as the lead single from the album on October 12, 2012. It peaked at number 75 on the UK Singles Chart.
"Don't Save Me" was released as the second single from the album on November 8, 2012. It peaked at 32 on the UK Singles Chart, the song also peaked at 66 in Australia, 28 in Belgium (Flanders region), and 70 on the Irish Singles Chart.
"Falling" was released as the third single from the album on February 12, 2013. It peaked at 30 on the UK Singles Chart and 86 in Australia.
"The Wire" was released as the fourth single from the album on August 9, 2013. It peaked at 12 in Australia and 16 on the UK Singles Chart.
"If I Could Change Your Mind" was released as the fifth single from the album on March 21, 2014. It peaked at 27 on the UK Singles Chart.
"My Song 5" was released as the sixth single from the album on August 15, 2014.
Upon its release, Days Are Gone received generally favorable reviews from music critics. At Metacritic, which assigns a weighted mean rating out of 100 to reviews from mainstream critics, the album received an average score of 79, based on 35 reviews. Ann Powers from NPR stated "HAIM's thoughtful, playful music is good for the radio, good for rock, and good for music lovers of all ages who need to carve out a little space to dream." Becca James of The A.V. Club gave the album a very positive review: "It could be an overstatement to say that if Days Are Gone is any indication of what's to come for Haim, the band is set." Matt James of PopMatters complimented all overall production "It'd be hard to truly dislike Haim. They're an eminently likeable, albeit slightly kooky, trio whose story already bears the frisson of legend. Three multi-talented siblings—Danielle, Alana and Este—who were baptised in the dark arts of rock 'n' roll by their own parents" and added [...] "It's not revolutionary, life-changing 'high art' but right here, right now Haim's sassy, enthusiastic, 'one for all' joie de vivre feels freshly invigorating, infectious ...basically, a drop o' the good stuff."
Jon Caramanica of The New York Times hailed the synthesized and the hooked production and compared the girls to the early years of Madonna, Pat Benatar, Sheena Easton and Laura Branigan: "There's the slightly sinister bubblyness of early Madonna, the erotic power of Pat Benatar, the breathlessness of Sheena Easton or Laura Branigan," and continued, "Haim lashes all of these together with force and glee, a rapturous throwback. “Days Are Gone” is as convincing as any major-label rock album this year, especially its first half, which is slick, confident and winningly breezy." Jody Rosen of Vulture praised the album's fusion of "everything from the Doobie Brothers to Janet Jackson to third-wave feminism" combined with "catchy four-minute-long songs." John Dolan of Rolling Stone awarded the album a three and-half-stars out of possible five "Their charming debut recalls the dancy side of Eighties Top 40 radio as an AstroTurf Eden of chewy synths, neon-cheese guitar quake and slick, airy melodies." In a less enthusiastic review, Andy Gill of The Independent gave the album three out of five stars, saying that the band has an "insubstantiality at their core." Philip Matusavage of musicOMH gave a mixed review, commenting, "Stretched to album length, Haim's shtick grows repetitive and the music is too frequently solid rather than inspired".
Stereogum ranked Days Are Gone at number eight on their "The 50 Best Albums of 2013" list, stating: "On their debut album, [Haim] bring Stevie Nicks float, Michael Jackson glide, and Debbie Gibson twinkle to the table, subsuming them all into the massive force of their collective personality. They're not indie, but if they were, indie would be lucky to have them."
Days Are Gone entered the Billboard 200 at number six with first-week sales of 26,000 copies. The album debuted at number one on the UK Albums Chart, selling 37,005 copies in its first week. On October 25, 2013, the album was certified silver by the British Phonographic Industry (BPI), denoting shipments of over 60,000 copies in the UK, and on December 27, 2013, was certified gold denoting shipments of over 100,000 copies.