"Teardrop" was first developed from a simple harpsichord riff picked out in the studio in April 1997. 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. 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 song, especially the instrumental portions at the beginning and the end, has been used in numerous TV programmes and movies. The bass drum beat, reminiscent of a heartbeat, samples the Les McCann song "Sometimes I Cry". From 2004 to 2012, it was used as the opening theme of the American medical drama series House. It is also featured as incidental music in a 2001 episode of the long-running ITV soap opera Coronation Street when Sarah Platt is chased. An instrumental version of the tune is also used in the first season episode of Prison Break, "Tonight". The song was used in the twenty-first season episode of The Simpsons, "Postcards from the Wedge".
The 12" release contains the same songs but in a different order. The cassette release contains an edited version of the original song, as well as the Scream Team remix and the B-side "Euro Zero Zero", but is missing the remix by Mad Professor.
José González covered "Teardrop" for his second album In Our Nature. The single was released across Europe on 12 November 2007. The single features the non-album instrumental B-side "Four Forks Ache." This version was also featured in the medical drama House M.D. in the episode "Wilson's Heart".