On paper, Oscar-winning director Martin Scorsese filming the legendary Rolling Stones in concert sounds brilliant and, on film, it is. Yes, there was dissing at the film’s Berlin Film Festival debut (something about no dish about the band?), but Shine a Light—as concert film extraordinaire—delivers big-time.

Similarities between director and subject might have something to do with this. Both Scorsese and the Stones are comfortably past 60, still working as hard as ever and, at their peaks, still indisputable masters of their respective disciplines.

And they share some common ground. Scorsese has incorporated many a Stones hit into his soundtracks, and music and film have enriched all their careers. Scorsese already has several music docs behind him, including The Last Waltz, featuring The Band, and No Direction Home: Bob Dylan. And the Stones are hardly strangers to the concert film, having been featured in several, including the classic Gimme Shelter. Mick Jagger himself produces and acts in films. And, hey, Keith Richards is a total film buff.

Still, Shine a Light required a Big Event—Bill Clinton’s birthday celebration for his entourage and Stones fans at New York’s Beacon Theatre—for this Scorsese/Stones mash-up. Filmmaker and rock stars both attracted top talent in their respective fields.

Besides supervising DP Robert Richardson, a swarm of well-known and Oscar-winning and nominated camera wizards (including Robert Elswit, Albert Maysles, Ellen Kuras and John Toll) captured the frenetic onstage action. On the music side, legendary sax player Bobby Keys is one of an impressive team of back-up musicians and Jack White and Christina Aguilera put in guest appearances. Strong back-up vocalists also lend their chops, but it’s the band who are always stunningly front and center, exploding on screen.

Shine a Light is all about the Stones and the preternatural charisma and energy of lead vocalist Jagger, the beneficiary of good hair, an expressive face that articulates every lyric, and a nimble, lithe body that further propels every sound. The music soars, thanks largely to the many hits served up with grand éclat, including staples like “Jumpin’ Jack Flash,” “Shattered,” “As Tears Go By,” “Tumblin’ Dice,” “Sympathy for the Devil,” “Brown Sugar” and “Satisfaction.”

Scorsese uses mostly medium and tight shots and rhythmic cutting that perfectly package the set-pieces and reveal the truths behind the Stones’ longevity—they share a passion for performance and a passion for one another. As Richards says about being onstage, “We don’t think when we’re up there; we feel.”

In a bit of a Pirandellian tease, Scorsese sometimes appears displaying Italian-American agita regarding the logistics of filming so challenging a project (so many cameras, so little space, etc.).

If The Last Waltz was elegant, this Scorsese doc is electric. Stones fans and pop enthusiasts across generations will be riveted by these kings of cool, these elder statesmen of androgyny.