The song was written by both alongside Savan Kotecha, Ilya and Max Martin, being produced by the latter two with Shellback, with Peter Carlsson serving as a vocal producer.
The song later peaked at number two, surpassing "The Way" as her highest-charting single in the United States.
"Problem" remained in the top ten of the Hot 100 for the first sixteen weeks of its chart run, making its number three debut on May 7, 2014 and dropping out of the top ten on August 27, 2014.
Internationally, the single debuted at the top of the charts in Ireland, New Zealand, Scotland and the United Kingdom, while peaking within the top ten of the charts in most other territories, including Australia, Canada, Sweden, Denmark, and Greece.
"Problem" became the first song to top the UK Singles chart based on both sales and streaming.
To promote the song, Grande performed it first at the 2014 Radio Disney Music Awards, followed by the 2014 iHeartRadio Music Awards, on The Ellen DeGeneres Show and at the 2014 Billboard Music Awards.
The song's accompanying music video was directed by Nev Todorovic and premiered on Vevo on May 30, 2014.
It won "Best Pop Video" at the 2014 MTV Video Music Awards and has been viewed more than 1 billion times.
As of 2016, it has sold 3.6 million copies in the US, and has been certified sex-tuple platinum by the Recording Industry Association of America (RIAA).
It is among the best-selling singles of all time, with combined sales and track-equivalent streams of 10 million units according to IFPI.
The single was originally set for release on March 25, 2014, but it was postponed due to Brown being sent to jail awaiting trial on assault charges.
Grande had met Azalea at the 2013 MTV Europe Music Awards where they had presented an award together, and hung out at Katy Perry's after party in Amsterdam, where they expressed interest in working together.
Big Sean, who is featured in Grande's previous single "Right There", also appears on the song uncredited as a background vocalist in which he provides the whisper-like vocals of the chorus although he is not a featured artist.
The line "one less problem without you" was inspired by an article from Cosmopolitan.
Azalea agreed to appear on the song and went in with producer Max Martin to write her own verse before recording it for the song.
A remix of the song was released on May 16, 2014 entitled the "Young California Remix" and features an additional rap verse from American rapper Problem.
A Spanglish version of the song was also released featuring Colombian rapper J Balvin for the Hispanophone market, making it the second collaboration between the two artists.
In August 11, a remix version by DJ Boss in Drama was released in Brazil featuring Brazilian pop singer Gretchen.
Mike Wass of Idolator described the song as "an odd blend of '90s pop and current urban trends but there's no denying that it's catchy."
Entertainment Weekly called the song a "dramatic reinvention," and also notes, "The idea that Grande was collaborating with bad girl Iggy Azalea prompted all kinds of speculation, and the result is more or less what everybody expected.
On Billboard Pop Songs, the song debuted at number 28 and reached number 21 in its second week on the chart.
"Problem" just missed the entry into the Billboard Radio Songs chart in its first week of availability. It officially entered in at number 30 on the chart, up 70% in audience impressions from 24 million to 41 million.
The song was released by Republic Records on April 28, 2014, as the lead single from Grande's second studio album My Everything (2014).
"Problem" is an uptempo dance-pop song with influences of R&B music, which comprises a melody based on drums, saxophone loops, and trumpets.
The chorus features uncredited background vocals from American hip hop artist Big Sean.
The song debuted at number three on the Billboard Hot 100 selling 438,000 copies in its first week on sale, earning Grande her biggest digital song sales week ever.