Carly Simon cemented her pop-star status with her third album, No Secrets, released in November 1972. She wrapped the LP's biggest hit, "You're So Vain," around what ended up becoming one of rock's most enduring mysteries.

The first single from No Secrets, "You're So Vain" topped the Billboard singles chart on Jan. 6, 1973, kicking off a three-week stay at No. 1 and beginning decades of speculation about who Simon was referring to in the lyrics. Songwriters vent about former lovers in their music all the time, but because Simon was known for writing particularly autobiographical songs – and because she tended to hobnob with the rich and famous – people really wanted to know who had inspired such withering (yet utterly laid-back) scorn.

One popular guess: Rolling Stones singer Mick Jagger, who would have made an appealing fit for a number of reasons, among them the fact that he had a glamorous love life to match Simon's (as well as a fabulous set of lips to rival her own). In addition, Jagger contributed uncredited background vocals during the sessions for "You're So Vain," a collaboration Simon said took place simply because "he happened to call at the studio. … I said 'We’re doing some backup vocals on a song of mine, why don’t you come down and sing with us?'"

"I didn't take the song as seriously as all that," Simon later reflected in an interview with Uncut. "It wasn't vengeance; it wasn't Anna Karenina. It was, 'From this point of view, you don't necessarily look as good as you think you look.' There's not an iota of hate in it. There may be much more of an iota of feeling hurt or rejected. ... I was definitely a romantic and my hopes were dashed. That led to the song."

For decades Simon coyly refused to reveal the identity of her inspiration. However, in 2015 the singer admitted to People that part of the song is about actor Warren Beatty. “I have confirmed that the second verse is Warren,” Simon noted in an interview discussing her memoir Boys in the Trees. The singer went on to explain that the track's other verses are about different men, despite the fact Beatty "thinks the whole thing is about him.”

Though fans may never know who Simon is singing about in those other verses, "You're So Vain" remains a staple of her repertoire. While she'd go on to arguably greater success with subsequent singles (including the James Bond song "Nobody Does It Better," which won an Academy Award), "Vain" is widely regarded as Simon's signature number.