Happy Mother's Day, Bebe Buell! These days, she's best known as the mom of actress Liv Tyler, whose father is Aerosmith's Steven Tyler. But Buell is also rather legendary as the mother of all rock-star girlfriends, having been linked with a rock 'n' roll Who's Who in the 1970s. Just don't call her a groupie.

A teenage model who became a Playboy Playmate of the Month in 1974, Buell lived with Todd Rundgren for several years after meeting him in 1972. They had an open relationship. As she writes in 'Rebel Heart,' her best-selling 2001 autobiography, Rundgren was sleeping with "nondescript road tramps" while she was working her way up the rock 'n' roll hierarchy. Models dating rock stars were still a novelty at the time, she writes: "Apres moi, le deluge."

For several years after Liv's birth in 1977, Rundgren acted as the girl's father, with Steven Tyler out of the mother's life and fighting drug addiction. Mick Jagger, another of Buell's lovers, supposedly questioned her attraction to Tyler, wondering why she wanted "the fake Mick" when she had the real one. Others with whom she was involved included Jimmy Page, David Bowie, Iggy Pop and Rod Stewart.

In the late '70s Buell began an on-again, off-again relationship with Elvis Costello. There's been much speculation about how deeply their bitter breakups inspired the singer's acid-tongued lyrics. Buell, Costello has suggested, claimed she was the muse for songs on his early albums 'Armed Forces' and 'This Year's Model,' when he'd already written the songs. She says his album 'Blood and Chocolate' was named for her craving at a certain time of the month.

More than two decades later, they're still bickering. "He wants people to think I'm crazy; it delights him," Buell wrote in her book. Costello has written in reply, "I wish I could say: 'I shall not dignify that with a response, but 'dignity' doesn't come into this story."

To Buell, she's the face that launched a thousand songs. She has claimed that Prince wrote 'Little Red Corvette' for her ("Bebe, you're much too fast"), despite the inconvenient truth that the two didn't know each other. But she was undoubtedly one of the inspirations for Penny Lane, the rock chick in 'Almost Famous': Director Cameron Crowe met Buell during a tour with Rundgren on a Rolling Stone assignment in the 1970s. (The leader of the fictitious band Stillwater, played by Jason Lee, is named Jeff Bebe.)

As a sometime performer herself, Buell cut a 1981 EP with members of the Cars, and she was instrumental in the formation of the '80s supergroup the Power Station, originally formed as her backing group by then-boyfriend John Taylor of Duran Duran. Today, she has a new single, 'Air Kisses for the Masses,' her first recording in almost 10 years. As a rock mama, she's had her ups and downs. After managing her daughter's early acting and modeling career, she was unceremoniously relieved of her duties. Too much mothering.