"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.
The song peaked at number two in Ireland, New Zealand and the United Kingdom, where it was released twice, once in 1985 and again in 1991.
Madonna has performed "Crazy for You" in three of her concert tours, The Virgin Tour in 1985, Re-Invention World Tour in 2004 and in some dates of Rebel Heart Tour in 2016.
The song is set in the key of E major.