"Teardrop" was first developed from a simple harpsichord riff picked out in the studio in April 1997. Andrew Vowles sent the demo to Madonna as he wanted her to record the vocals for the song (the band had previously worked with her on their 1995 reworking of the song "I Want You"). The two other band members Robert Del Naja and Grantley Marshall wanted Elizabeth Fraser of the Cocteau Twins to record the vocals, feeling her ethereal style suited the mournful melody and feel of the piece. Madonna was very keen to record the vocals, and was disappointed when the two-to-one vote went in Fraser's favour.
Fraser wrote the song's lyrics, inspired by the works of French philosopher Gaston Bachelard. While recording the song on 29 May 1997, she found out that her once-close friend, Jeff Buckley, had drowned. "That was so weird ... I'd got letters out and I was thinking about him. That song's kind of about him – that's how it feels to me anyway."
The single peaked at number 16 in Australia. It placed number 22 in the Triple J Hottest 100 of All Time in 2009. It reached the top 10 in the UK and is the only Massive Attack track to do so. It was certified Silver by the BPI on 22 July 2013.