It was released as the second single from the band's second studio album Happy to You (2012) on 14 May 2012, through Axtone, Columbia, Downtown and Universal Republic.

Musically, "The Wave" is an electropop song with marching band influences and autoharp, military drum and piano instrumentation.

"The Wave" was written and produced by Miike Snow's three members: Christian Karlsson, Pontus Winnberg and Andrew Wyatt.

[2][3] Karlsson told Billboard that his favorite part of the song occurs during the second verse, in which all band members are hitting the drums simultaneously.

Initially, Thomas Gold's remix was released exclusively on the online music store Beatport on 14 May 2012, through Axwell's record label Axtone.

The release features the radio edit of the original song and remixes by Gold, Brodinski and Style of Eye.

[7] Prior to the release of both their second album and single, the band announced in February 2012 that they were going to play two UK shows in London and Manchester.

[14] In an interview for Complex, Wyatt said that the song is built in "tsunami form", stating that "the real pay-off" does not come until the final refrain.

[15] According to critic Josh Modell of Spin, the song "dips its toes in the kind of Brit-rock purveyed by Elbow but mixes in some organic, tribal fun à la Yeasayer".

Adam Markovitz of Entertainment Weekly named it one of the best tracks on Happy to You,[18] while Will Salmon of Clash and Amber Genuske of HuffPost called it a standout.

's Ashley Hampson deemed it "incredibly catchy", writing that it "capitalize[s] on the falsetto musings of vocalist Andrew Wyatt".

[14] The writer praised the piano and marching drums for "giving the song a sense of direction that the opener lacked".

[22] Chris Schulz of The New Zealand Herald said that the song, alongside the album tracks "Paddling Out" and "Bavarian #1 (Say You Will)", "will swirl around in your head for days and demand repeat plays".

[29] Picking up where the first part left of, the video follows Jean Noel, a human man who has received plastic surgery from aliens to be transformed into the "perfect specimen".

[30] In an interview for The Creators Project, Nilsson explained how the videos were conceptualized: "The concept of this was born after long evenings of me and the band talking about gene technology in contemporary science.