In the United States, it became Blur's first single since "Song 2" to enter the Modern Rock Tracks chart, where it reached number 22.

[2][3] The remaining members of Blur decided to carry on recording, travelling to Morocco to continue developing the album, with the intention to "escape from whatever ghetto we're in and free ourselves by going somewhere new and exciting".

"[7] Musician Norman Cook, commonly known as Fatboy Slim, was invited to collaborate on the project, as he was a "really nice injection of fresh energy at a point in the proceedings when we needed one, and he fundamentally understands music", according to James.

Hiller recalled that the drum sound for "Crazy Beat" is just the effects of a room made of a marble floor, tiled walls and a concrete ceiling, which provided a "really banging reverb".

[5] In 2015, Albarn declared that he regretted including "Crazy Beat" on Think Tank, rather than a song titled "Me, White Noise", attributing his decision to outside influences at the time; the latter was actually on the record, hidden as a prologue thanks to a digital chicanery which revealed the track if the CD was rewound.

[12] The single's cover art features a satirical portrait of the British royal family by English graffiti artist Banksy; the mural was painted on a building in Stoke Newington.

[13] In the United States, Virgin Records serviced the track to alternative radio stations on 17 March 2003, as the lead single from the album in the region.

"[34] Steve Lowe from Q deemed the track as "the album's prime Fatboy Slim moment", and stated that it was "surely a hit".

[36] Bram Teitelman of Billboard stated that "the combination of Cook's production and the aggressive guitar riff gives 'Crazy Beat' a shot of adrenaline, and it seems destined to follow in the footsteps of 'Song 2' as a fixture at sporting events.

[37] Kitty Empire from The Observer commented that the song was not "Blur's finest hour, nor Norman Cook's, but it will reassure Blur-watchers (and the record company) that the band haven't entirely disappeared up Albarn's world music collection.

"[25] Classic Pop's Steve Harnell described it as "airhead fun", but felt that Think Tank's high points were "mostly found elsewhere".

[21] Alexis Petridis from The Guardian called Cook's tracks on Think Tank, including "Crazy Beat", as "cluttered-sounding collaborations" which "fall short of their ambition", as well as "a disappointment".

[44] Devon Powers of PopMatters described it as an "energetic, punked-out rocker", although "as much as this song might appeal to the neo-DIY set — complete with its jumpy chorus and lively melody — Blur are anything but".

[47] Ben Gilbert from Dotmusic condemned the track, pointing out its "lazy, predictable, sub-'Song 2' primal noise and pointless, throwaway chorus", and asserting that it was "Think Tank's weakest moment by some considerable distance".

The first was directed by animation collective Shynola in late March 2003 at Ealing Studios in London and premiered through MTV's website the following month.

[58] The visual sees the band performing the song in a pub as a green audio waveform comes to life while vibrating in time with the music.

[59] An alternate video was directed by John Hardwick;[12] it shows four women performing a dance routine to the song, wearing matching brown dresses and blonde wigs.

Although MTV reported Blur was annoyed to play the song on television shows at the time of its release,[9] "Crazy Beat" was performed on Top of the Pops,[60] Headliners[61] and Supersonic.