Eurythmics had their fair share of hits, and several remain resonant of their age – in particular, "Sweet Dreams (Are Made of This)," "Here Comes the Rain Again" and "Would I Lie to You?" But their true legacy lies not in the singles, or even the distinctive videos, but in their tireless search for the new.

What made Annie Lennox and Dave Stewart so intriguing was that each successive album, sometimes from song to song, could be so consistently eclectic. These fearless experiments didn't always pay off on the charts and didn't always fill up football stadiums. But say this for Eurythmics: They were never, ever boring.

You cued up a Eurythmics LP expecting to be challenged, and they delivered. Even when they broke through to wider fame, as on "Sweet Dreams," listeners had to let go of their built-in expectations to discover something different. After all, Eurythmics' only chart-topping U.S. single doesn't have verses, only choruses and pre-choruses.

They didn't even split up conventionally, initially taking a decade-long post-'80s break – and then going silent again after 1999's Peace without ever confirming whether Eurythmics would (or would not) work together again. Can this iconoclastic streak carry Eurythmics to a Rock & Roll Hall of Fame induction? Here are five reasons why it should.

They Were No Overnight Success

"Sweet Dreams (Are Made of This)" made Eurythmics feel like an overnight smash, but it took about eight years to get there. Stewart met Lennox at a restaurant where the singer was waitressing after she dropped out of the Royal Academy of Music because it wasn't the right fit. They quickly coupled up, both personally and professionally. Their first band together, led by earlier Stewart associate Peet Coombes, was a punkier group called the Catch. One failed single later, they reworked the lineup and changed direction and band names, becoming the Tourists. These purveyors of melancholy power-pop stayed together a bit longer, sending a pair of songs into the U.K. Top 10. It didn't last, but the couple was learning the ropes. "Annie and I moved into a squat above a record shop," Stewart told Forbes. In the Tourists, "Peet wrote all the songs. We made three albums and toured everywhere — Australia, America, Europe — and squeezed into a little van." Lennox and Stewart decided to strike out on their own after the Tourists' 1980 LP Luminous Basement flopped, naming their new group after a rhythmic method of teaching music to kids. They then took the first of many, many sudden musical turns in 1981 by connecting with well-respected krautrock producer Conny Plank. "Annie and I were living together as a couple of whole time," Stewart added. "But when we decided to be a duo making music, we went into a completely different world — a world that we wanted to do, that was more experimental."

They Were Self-Made Stars

The ever-inventive In the Garden, despite whatever star power that Plank might have possessed, basically sank without a trace. "Never Gonna Cry Again" finished at No. 63 in the U.K., but their album failed to chart anywhere. RCA declined to fund a follow-up, leaving Stewart to finance the sessions himself – primarily through a personal loan from a bank. Eurythmics workshopped their next batch of songs in a London warehouse, rather than running up studio bills for proper sessions. Most of the resulting LP, which became the gold-selling U.S. Top 20 smash Sweet Dreams (Are Made of This), was recorded on second-hand equipment – including a rudimentary eight-track TEAC machine. There was a loose sense of discovery, as occasional co-producer Adam Williams taught them how to get the most out of the aging tech they were surrounded by. Lennox created the lyrical accompaniment for "Sweet Dreams" in a matter of minutes after improvising bass riffs, loops, and string motifs on a Roland Juno-6 synth, while Stewart created a pattern on the drum machine. The results finally dislodged the Police's "Every Breath You Take" from the No. 1 spot after seven weeks. By then, however, Eurythmics were already tucked away inside London's Church Studios with engineer Jon Bavin, at work on Touch. Recording on an upgraded 24-track machine, they completed their third LP in just three weeks.

Their Partnership Transcended Heartbreak

Lennox and Stewart lived together while in the Tourists, connecting so deeply on a musical level that they decided to form Eurythmics after its precursor band unraveled. By then, however, their relationship had fallen apart. "I had lived through a lot of other people and through Dave, and I wanted to sort of break away from that," Lennox told the Los Angeles Times in 1986. "But I knew creatively I didn't want to work with anybody except Dave. So, there was this strange tension – the pain of the breakup and the excitement of working together on the music. In some ways, that tension has never really gone away. There is always something that brings an edge to what we do." Years later, she included a lyric about a couple "who couldn't be together, and who could not be apart" in the U.K. Top 30 hit "17 Again," seemingly touching on her unusual working relationship with Stewart. They've since added to their many shared successes, as Stewart won a Golden Globe and Lennox claimed an Academy Award. Eurythmics just did all of it in a different order: "Most couples get famous and then break up," Stewart told the Times, with a chuckle. "But we broke up and then got famous."

They Helped Us Celebrate R&B Again

Eurythmics began their career alongside producer Conny Plank, who'd worked with Brian Eno, Can, Kraftwerk, Ultravox, and Neu!, among others. But they never remained locked into any one musical subset, notably embedding a quite-surprising R&B thread throughout their most celebrated period. "There Must Be an Angel," Eurythmics' first chart-topping U.K. single, showcased a high-spirited harmonica solo by Stevie Wonder. (The Motown star reportedly nailed it in one 4AM take.) Aretha Franklin duetted with Lennox on "Sisters Are Doin' It for Themselves." Not exactly an expected move in the early-MTV era. "Right by Your Side," another Top 10 U.K. hit, featured a turn on sax by Martin Dobson, who toured with the likes of Marvin Gaye, the Temptations and the Supremes, among others. "Would I Lie to You" included bass work from Nathan East, who collaborated with Wonder and Michael Jackson. "'Would I Lie to You' came out and of course, America got it straight away,” Stewart told Forbes, "because it sounded like some Stax R&B thing. If you analyze Eurythmics records, we're talking about things that are all on the same record — 'Missionary Man' and 'Sisters Are Doin' It for Themselves' — and you put them side by side, you go, 'Wow, this is the same group — all these different songs.'" Ex-Gap Band singer Charlie Wilson is also on the latter-day Eurythmics track "Revival."

Their Music Has Held Up

Eurythmics music still leaps out of speakers because even their most popular songs aren't traditionally commercial. Lennox and Stewart didn't chase trends so much as create them. At the same time, there is a sturdy classicism about it all. The No. 4 U.S. smash "Here Comes the Rain Again" didn't need to be dressed up with the plasticine reverb and building-toppling gated drums of the period to connect. A vivid string arrangement by Michael Kamen and Lennox's dramatic (but not overly dramatic) vocals do most of the work. "People thought we were an electronic duo that came to America with this new wave synth-pop," Stewart told Billboard, "but actually we insisted when we were writing our songs that you could play them with just a guitar and voice, or piano and voice. I think the '80s were seen as this kind of pop music – quite disposable, blah, blah – and yet it's still heard all over the place, our music. But it was the same with Motown, wasn't it? 'Oh, this is a lot of throwaway pop music,' but still, when you hear them they sound fantastic." As if to prove the point, Lennox has movingly performed "Here Comes the Rain Again" with only a delicate piano accompaniment.

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