Their debut album Whatever People Say I Am, That's What I'm Not, released in early 2006, became the fastest-selling debut album in British music history, surpassing Oasis's Definitely Maybe and remains the fastest-selling debut album for a band in the UK. Since then the band have released two more albums: Favourite Worst Nightmare (2007) and Humbug (2009). The band is currently in the studio, recording their fourth album, expected to be released in 2011.

Arctic Monkeys are heralded as one of the first acts to come to the public attention via the Internet (fan-based sites rather than from the band), with commentators suggesting they represented the possibility of a change in the way in which new bands are promoted and marketed.

In 2001, neighbours Alex Turner and Jamie Cook learned how to play the guitar. Later, after the two boys received guitars as Christmas presents, they formed a band with Turner's schoolmates Andy Nicholson and Matt Helders. Nicholson already played bass guitar, so Helders ended up playing drums — "that was all that were left... they all had guitars so I bought a kit after a bit." According to an interview with Blender magazine, Turner was not the original singer of the band, but instead, Glyn Jones, another attendee of Stocksbridge High School, used to be the frontman. Jones said that he and Turner "were bored [after our GCSE exams] so we started writing a song about a geek in our year...", and that he left the band because he "did not have the dedication to take it any further... to me we were just a gang of kids messing around because we were bored." Although reports suggested they named themselves after Helders' uncle's (or even father's) band, Helders later admitted that "so many people asking us that in the UK, so we just started making stories up", and that he just didn't have the heart to tell the original reporter he'd been lying.

They began rehearsing at Yellow Arch Studios in Neepsend, and played their first gig on 13 June 2003 at The Grapes in Sheffield city-centre.

After a few performances in 2003 the band began to record demos at 2fly studios in Sheffield, 17 songs were demoed in all and the collection now known as 'Beneath the Boardwalk' and burn them into CDs to give away at gigs, which were promptly file-shared amongst fans. The group did not mind, saying "we never made those demos to make money or anything. We were giving them away free anyway — that was a better way for people to hear them. And it made the gigs better, because people knew the words and came and sang along.", admitting that they did not even know how to get their songs onto the Internet. When asked about the popularity of the band's MySpace site in an interview with Prefix Magazine, the band said that they were unaware what it was, and that the site had originally been created by their fans. "[When we went number one in England] we were on the news and radio about how MySpace has helped us. But that's just the perfect example of someone who doesn't know what the fuck they're talking about. We actually had no idea what it was."

They began to grow in popularity across the north of England, receiving attention from BBC Radio and the British tabloid press. A local amateur photographer, Mark Bull, filmed the band's performances and made the music video to "Fake Tales of San Francisco", releasing it on his website, alongside the contents of Beneath the Boardwalk — a collection of the band's songs which he named after a local music venue. In May 2005, Arctic Monkeys released their first single, Five Minutes with Arctic Monkeys, featuring the songs "Fake Tales of San Francisco" and "From the Ritz to the Rubble". This release was limited to 500 CDs and 1000 7" records, but was also available to download from the iTunes Music Store. Soon after, the band played at the Carling Stage of the Reading and Leeds Festivals, reserved for less known or unsigned bands. Their appearance was hyped by much of the music press and the band was watched by an unusually large crowd. The critically-acclaimed performance included spontaneous singalongs of tracks that were only available as demos on the Internet.

The band refused to change their songs to suit the industry and resisted signing to a record label — "Before the hysteria started, the labels would say, 'I like you, but I'm not sure about this bit, and that song could do with this changing...' We never listened." Their cynicism towards the industry was such that record company scouts were refused guaranteed guest list entry for their gigs, a move described by MTV Australia as "We've got this far without them — why should we let them in?". The success of the strategy was illustrated with a series of sell-out gigs across the UK and Ireland.

Eventually, they signed to Domino in June 2005. The band said they were attracted to the "DIY ethic" of Domino owner Laurence Bell, who ran the label from his flat and only signed bands that he liked personally. The UK's Daily Star reported that this was followed in October by a £1 million publishing deal with EMI and a £725,000 contract with Epic Records for the United States. Arctic Monkeys denied this on their website, dubbing the newspaper "The Daily Stir". However, Domino have licensed the Australian and New Zealand publishing rights to EMI and the Japanese rights to independent label Hostess.

Their first single with Domino, "I Bet You Look Good on the Dancefloor", was released on 17 October 2005 and went straight to #1 on the UK Singles Chart, beating Sugababes and Robbie Williams. Four months later, they made their first appearance on the cover of NME. Their second single, "When the Sun Goes Down" (previously titled "Scummy"), released on 16 January 2006, also went straight to #1 on the UK Singles Chart, selling 38,922 copies and taking over that position from Shayne Ward. The band's success without marketing or advertising led some to suggest that it could signal a change in how new bands achieve recognition.

The band finished recording their debut album, Whatever People Say I Am, That's What I'm Not, at Chapel Studios in Lincolnshire in September 2005. Whatever People Say I Am, That's What I'm Not became the fastest selling debut album in UK chart history, selling 363,735 copies in the first week. This smashed the previous record of 306,631 copies held by Popstars by Hear’Say, and sold more copies on its first day alone — 118,501 — than the rest of the Top 20 albums combined.