"Burning Up" is a song by American singer Madonna from her eponymous debut studio album Madonna (1983). It was released as the album's second single on March 9, 1983, in some countries as a double-A side single with "Physical Attraction", another song from the album. The song was presented as an early recorded demo by Madonna to Sire Records who green-lighted the recording of the single after the first single "Everybody" became a dance hit. Madonna collaborated with Reggie Lucas, who produced the single while John Benitez provided the guitar riffs and backing vocals. Musically, the song incorporates instrumentation from bass guitar, synthesizers and drums, and the lyrics talk of the singer's lack of shame in declaring her passion for her lover.

Released with "Physical Attraction" on the B side, the song was given mixed reviews from contemporary critics and authors, who noted the song's darker, urgent composition while praising its dance beats. The single failed to do well commercially anywhere, except the dance chart in the United States, where it peaked at three, and the Australian charts, where it was a top 20 hit. After a number of live appearances in clubs to promote the single, it was added to the set-list of the 1985 Virgin Tour. An electric guitar version was performed on the 2004 Re-Invention World Tour and the 2015–16 Rebel Heart Tour.

The accompanying music video of the song portrayed Madonna in the classic submissive female positions, while writhing in passion on an empty road, for her lover who appeared to come from her behind on a car. The video ended showing Madonna driving the car instead, thereby concluding that she was always in charge. Many authors noted that the "Burning Up" music video was a beginning of Madonna's depiction of her taking control of a destabilized male sexuality.

In 1982, Madonna was living in New York and trying to launch her musical career. Her Detroit boyfriend, Steve Bray, became the drummer for her band. Abandoning hard rock, they were signed by a music management company, Gotham records, and decided to pursue music in the funk genre. They soon dropped those plans. Madonna carried rough tapes of three songs with her: "Everybody", "Ain't No Big Deal" and "Burning Up". Madonna presented "Everybody" to the DJ Mark Kamins who, after hearing the song, took her to Sire Records, where she was signed for a single deal. When "Everybody" became a dance hit, Sire Records decided to follow up with an album for her. However, Madonna chose not to work with either Bray or Kamins, opting instead for Warner Brothers producer Reggie Lucas. Michael Rosenblatt, the A&R director of Sire Records, explained to Kamins that they wanted a producer who had more experience in directing singers; hence they appointed Lucas. He pushed Madonna in a more pop direction and produced "Burning Up" and "Physical Attraction" for her.

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