The Last Shadow Puppets' debut album, The Age of the Understatement, was released in April 2008, shortly after Turner had moved from Sheffield to east London.
Co-written by Turner and Kane, the album was recorded in the Loire Valley, France and featured string arrangements by Owen Pallett.
Alexa Chung, dating Turner since mid-2007, featured in the music video for "My Mistakes Were Made For You".
Hogan of Pitchfork noted that, lyrically, Turner was "moving from his anthropologically detailed Arctics brushstrokes to bold, cinematic gestures."
Petridis of The Guardian detected "the audible enthusiasm of an artist broadening his scope" and praised "a certain fearlessness on display".
During a tour with the London Philharmonic Orchestra, Turner said Kane's presence gave him "somewhere to hide" on stage.
The Last Shadow Puppets gave a surprise performance at Glastonbury Festival, with both Matt Helders and Jack White making guest appearances.
Alison Mosshart performed with the band at the Olympia in Paris, and provided vocals for a B-side.
Also in 2008, Turner formed a covers band with Dev Hynes for a one-off show in London and recorded a spoken word track "A Choice of Three" for Helders' compilation album Late Night Tales.

Turner has described Arctic Monkeys' third album, Humbug, released in August 2009, as "a massive turning point" in the band's career.
They travelled to Joshua Tree, California to work with producer Josh Homme of Queens of the Stone Age; it was the band's first experience of working in a studio for extended period of time.
Homme has said the album's heavier sound was initiated by the band themselves, while he encouraged Turner to embrace longer guitar solos and to develop his newfound "crooning" style of singing.
While Petridis of The Guardian found some lyrics "too oblique to connect", he was impressed by the band's "desire to progress".
He described "Cornerstone" as a "dazzling display of what Turner can do: a fabulously witty, poignant evocation of lost love."
Joe Tangari of Pitchfork felt the album was a "legitimate expansion of the band's songwriting arsenal" and described "Cornerstone" as the highlight.
During a break in the UK Humbug tour, Turner joined Richard Hawley on stage at a London charity concert, and played a seven-song acoustic set.
Homme joined Arctic Monkeys for a live performance in Pioneertown, California.

While living in Brooklyn, New York, where he moved with Chung in the spring of 2009, Turner wrote an acoustic soundtrack for the coming-of-age feature film Submarine (2010); it was released as an EP in March 2011.
Director Richard Ayoade initially approached Turner to sing cover versions but, instead, he recorded six original songs in London, accompanied by James Ford and Bill Ryder-Jones.
Two of the songs had already been written; Turner wrote the rest after watching dailies from the film set.
The songs existed within the world of the film as a mixtape made by the main character's father.
Paul Thompson of Pitchfork felt "Turner's keen wit and eye for detail" had created a "tender portrayal" of adolescent uncertainty.
 Ben Walsh of The Independent said the "exquisite" soundtrack was "reminiscent" of Cat Stevens's work on Harold and Maude.
In 2014, the Submarine soundtrack appeared on The Times's list of 100 Soundtracks to Love.
Turner also co-wrote six songs for Miles Kane's debut solo album Colour of the Trap (2011) and co-wrote Kane's standalone single "First of My Kind" (2012).

Turner wrote Arctic Monkeys' fourth album, Suck It and See, in New York and met up with his bandmates and James Ford for recording sessions in Los Angeles.
Marc Hogan of Pitchfork enjoyed the album's "chiming indie pop balladry" and "muscular glam-rock".
Petridis of The Guardian remarked that Turner's new lyrical style of "dense, Dylanesque wordplay is tough to get right.
More often than not, he pulls it off.
There are beautifully turned phrases and piercing observation."
Richard Hawley co-wrote and provided vocals for the B-side, "You and I", and performed the song with the band at the Olympia in Paris.
Turn
The Last Shadow Puppets' debut album, The Age of the Understatement, was released in April 2008, shortly after Turner had moved from Sheffield to east London. Co-written by Turner and Kane, the album was recorded in the Loire Valley, France and featured string arrangements by Owen Pallett. Alexa Chung, dating Turner since mid-2007, featured in the music video for "My Mistakes Were Made For You". Hogan of Pitchfork noted that, lyrically, Turner was "moving from his anthropologically detailed Arctics brushstrokes to bold, cinematic gestures." Petridis of The Guardian detected "the audible enthusiasm of an artist broadening his scope" and praised "a certain fearlessness on display". During a tour with the London Philharmonic Orchestra, Turner said Kane's presence gave him "somewhere to hide" on stage. The Last Shadow Puppets gave a surprise performance at Glastonbury Festival, with both Matt Helders and Jack White making guest appearances. Alison Mosshart performed with the band at the Olympia in Paris, and provided vocals for a B-side. Also in 2008, Turner formed a covers band with Dev Hynes for a one-off show in London and recorded a spoken word track "A Choice of Three" for Helders' compilation album Late Night Tales.
Turner has described Arctic Monkeys' third album, Humbug, released in August 2009, as "a massive turning point" in the band's career. They travelled to Joshua Tree, California to work with producer Josh Homme of Queens of the Stone Age; it was the band's first experience of working in a studio for extended period of time. Homme has said the album's heavier sound was initiated by the band themselves, while he encouraged Turner to embrace longer guitar solos and to develop his newfound "crooning" style of singing. While Petridis of The Guardian found some lyrics "too oblique to connect", he was impressed by the band's "desire to progress". He described "Cornerstone" as a "dazzling display of what Turner can do: a fabulously witty, poignant evocation of lost love." Joe Tangari of Pitchfork felt the album was a "legitimate expansion of the band's songwriting arsenal" and described "Cornerstone" as the highlight. During a break in the UK Humbug tour, Turner joined Richard Hawley on stage at a London charity concert, and played a seven-song acoustic set. Homme joined Arctic Monkeys for a live performance in Pioneertown, California.
While living in Brooklyn, New York, where he moved with Chung in the spring of 2009, Turner wrote an acoustic soundtrack for the coming-of-age feature film Submarine (2010); it was released as an EP in March 2011. Director Richard Ayoade initially approached Turner to sing cover versions but, instead, he recorded six original songs in London, accompanied by James Ford and Bill Ryder-Jones. Two of the songs had already been written; Turner wrote the rest after watching dailies from the film set. The songs existed within the world of the film as a mixtape made by the main character's father. Paul Thompson of Pitchfork felt "Turner's keen wit and eye for detail" had created a "tender portrayal" of adolescent uncertainty.  Ben Walsh of The Independent said the "exquisite" soundtrack was "reminiscent" of Cat Stevens's work on Harold and Maude. In 2014, the Submarine soundtrack appeared on The Times's list of 100 Soundtracks to Love. Turner also co-wrote six songs for Miles Kane's debut solo album Colour of the Trap (2011) and co-wrote Kane's standalone single "First of My Kind" (2012).
Turner wrote Arctic Monkeys' fourth album, Suck It and See, in New York and met up with his bandmates and James Ford for recording sessions in Los Angeles. Marc Hogan of Pitchfork enjoyed the album's "chiming indie pop balladry" and "muscular glam-rock". Petridis of The Guardian remarked that Turner's new lyrical style of "dense, Dylanesque wordplay is tough to get right. More often than not, he pulls it off. There are beautifully turned phrases and piercing observation." Richard Hawley co-wrote and provided vocals for the B-side, "You and I", and performed the song with the band at the Olympia in Paris. Turn
Alex Turner