It wasn’t that rock music didn’t exist before The Rolling Stones—it did. But it didn’t exist at quite the same scale, or with the same reach, or the same sheer attitude that made the Stones so seismic. You wonder if it had something to do with their otherness, as though the fact that the American sounds they emulated—blues, country, R&B—didn't belong to them made them both more reverential and more free to explore. Like excavations from an archaeological dig, the band’s best music played out like a conversation between present and past, finding fresh meaning and connections in sounds that feel classic, bygone. Mick Jagger once said he’d rather be dead than singing “Satisfaction” at 45. Certainly there were other artists of his generation who took the same attitude, figuratively and otherwise. Un-rock as it may be, The Rolling Stones decided to live.

Formed in 1962 by singer Jagger and guitarist Keith Richards (Richards spotted Jagger carrying Muddy Waters and Chuck Berry records on a train platform), the band—which went on to include jazz drummer Charlie Watts and bassist Ron Wood, among others—became one of the spearheads of the British Invasion, bad boys to The Beatles’ teddy bears. They toyed with folk and psychedelia in the mid-'60s (“Ruby Tuesday,” “Mother’s Little Helper”), but always circled back to something grittier, darker, the “Under My Thumb”s and “Paint It Black”s.

With some exceptions (including The Beatles’ famous live farewell at Shea Stadium), the idea of “arena rock” didn’t really exist until the Stones: There wasn’t the infrastructure, the technical capacity. As classic as their late-’60s and ’70s albums are (the country sprawl of Beggars Banquet and Exile on Main St., the swagger of Some Girls), they made their legacy on stage, scaling up the sweaty rush of small clubs to hockey rinks and football stadiums, using the studio as a place to refine instead of retreat.

In commemoration of Mick Jagger’s 75th birthday, a German entomologist persuaded his colleagues to name several fossils after members of the band—a singular tribute, not to mention a loving jab at their longevity. Jagger took his 76th birthday off; the next night, the band was back on tour.