It was the early 1960s, and England's youth, inspired by American rock 'n' roll and rhythm and blues, was finding its own sound. Bands were forming throughout the land. Some would endure in memory, legacy or influence-the Yardbirds, the Kinks, even the Beatles-but one would go on and on and on to become the self-proclaimed (and generally acclaimed) Greatest Rock and Roll Band in the World. The Rolling Stones formed precisely a half century ago, and are still at work-or, rather, at play, celebrating 50 years of phenomenal music and a journey as raucous as "Jumping Jack Flash." LIFE's cameras were there early and have been there since, capturing all the ragged glory. The same editors who produced a bestselling book on the Beatles now look at the long history of the Stones: the mysterious death of founder Brian Jones, the essential push-pull relationship of Jagger and Richard, the '60s signpost that was Altamont, the later glam and then the welcomed return to roots. Lynn Goldsmith's photography is here, and so is that of Bill Eppridge and other LIFE shooters on the beat. In special sections, the legendary tour chronicled in the documentary film "Gimme Shelter" is revisited with stills from the film (including the crucial moment at Altamont), and the current lives of Mick and Keith (Johnny Depp's best friend! New York Times bestselling author!) are shown in their colorful splendor. There are funny moments (the early Stones with TV host Dean Martin, who just doesn't get it, when they first fail-miserably-to "conquer America") and many thrilling ones. This special edition of LIFE commemorating the Stones at 50 chronicles how the band not only captured the hearts and minds of this country's rock fans, but the world's.