Initially Warner Bros. Records did not want the song to be released as a single, since they believed that it would take away the attention from Madonna's second studio album Like a Virgin (1984). In the end, Peters and Guber convinced Warner officials to greenlight its release. "Crazy for You" ushered a new musical direction for Madonna, as she had not previously released a ballad as a single. The track features instrumentation from snare drums, harp, bass synthesizer and electric guitar. Lyrically, the song speaks of a sexual desire between two lovers and consists of innuendos.
"Crazy for You" received positive response from music critics and earned Madonna her first Grammy Award nomination in the Best Female Pop Vocal Performance category in 1986. The song became Madonna's second number-one single on the U.S. Billboard Hot 100, and reached the top position in the charts of Australia and Canada as well. It also peaked at number two in Ireland, New Zealand and the United Kingdom, where it was released twice, once in 1985 and again in 1991.