Eurythmics invented their very own sound, a fusion of chilly synth-pop with hot-blooded soul. The enduring power of a handful of their hits—along with singer Annie Lennox’s striking, gender-bending self-presentation—made them one of New Wave’s most iconic acts. But the duo of Lennox and Dave Stewart never fit comfortably into any box, not even one of their own making. The two met in London in the mid-’70s, fell in love, and formed a group called The Tourists, putting out three albums of punkish power pop between 1979 and 1980. When the group split up, the pair—now friends—reformed as Eurythmics. On their debut album, 1981’s adventurous In the Garden, they fused post-punk with Krautrock, assisted by Can’s Holger Czukay and Jaki Liebezeit. They came into their own with 1983’s Sweet Dreams (Are Made of This): Pairing Lennox’s husky, powerhouse voice with bass synths and drum machine, the title track is a spellbinding summation of the group’s eerie power. They defied the sophomore slump with the mournful, string-kissed “Here Comes the Rain Again,” off Touch, their second album that year. Where that song proved their pop-savvy, other tracks branched into spindly electro-funk, Caribbean rhythms, and smoldering torch songs. Eurythmics would display a similar range on four more LPs (futuristic dance pop, adult-contemporary ballads, amped-up soul) and the 1984 (For the Love of Big Brother) soundtrack before adjourning to pursue solo careers, then reuniting for 1999’s Peace. Their legacy—beyond those two or three songs that are as indelible as anything the ’80s gave us—is a songbook that’s as versatile as it is emotional.