Burning Up” is a song by American singer-songwriter Madonna from her self-titled debut album. 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”. 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.