"Crazy Stupid Love" received generally favourable reviews from music critics, whom praised its instrumentation, the song's catchiness and Tempah's appearance.

To promote the song, an accompanying music video was released on 9 June 2014, which sees Cole performing the track in an underground club, while Tinie Tempah also makes a cameo.

[11] On 27 May 2014, in an interview with Hello!, Cole announced that her fourth studio album would be released in November, preceded by lead single "Crazy Stupid Love", featuring Tinie Tempah.

[14] The single's cover art features Cole wearing "a gold bodysuit whilst her hair galavnated around her face", as noted by Metro's Hanna Gale.

[18] Lewis Corner of Digital Spy awarded the song 3.5 stars out of 5, and commented: "Sure, the lyrics are laden with sweet nothings and clichéd sentiments, but while Mrs Fernandez-Versini [Cheryl] may be swirling in mushy marital bliss right now, she hasn't sacrificed any of that star-quality sassiness to pull it off.

"[17] Maggie Pannacione of Artist Direct was very complimentary with the song, calling it "crazy catchy, with its pop neo-sax, handclaps, percussion and fingersnaps.

"[19] Brendon Veevers of Renowned for Sound claimed that the song "has a JLo/Beyoncé-ish vibe running through it in terms of its quick delivered, toe-tapping structure while Brit rapper Tinchy Stryder adds an effortless rap licking to the number nearing its end as horns toot left, right and centre allowing for the song to dip its toes in almost Latino-pop territory.