“That sense of the magazine editor’s hands on the magazine — that’s what’s going to get lost here,” he said. “I don’t know who’s going to be able to step in and do that anymore.”

Wenner Media has hired bankers to explore its sale, but the process is just beginning. BandLab’s stake in the company could also complicate matters. Neither Jann nor Gus Wenner would name any potential buyers, but one possible suitor is American Media Inc., the magazine publisher led by David J. Pecker that has already taken Us Weekly and Men’s Journal off Wenner Media’s hands.

The Wenners said that they expected a range of opportunities, and Jann Wenner said he hoped to find a buyer that understood Rolling Stone’s mission and that had “lots of money.”

“Rolling Stone has played such a role in the history of our times, socially and politically and culturally,” he said. “We want to retain that position.”

Jann Wenner tried his hand at other magazines over the decades, including the outdoor lifestyle magazine Outside and Family Life. But it was Rolling Stone that helped guide, and define, a generation.

“Who lives through the ’60s, ’70s, ’80s and ’90s and cannot be somehow wistful at this moment?” said Terry McDonell, a former top editor at Rolling Stone who also ran other Wenner magazines.

Rolling Stone filled its pages with pieces than ran in the thousands of words by standard bearers of the counterculture, including Hunter S. Thompson — whose “Fear and Loathing in Las Vegas” was published in the magazine in two parts — and Tom Wolfe. It started the career of the celebrity photographer Annie Leibovitz, who for many years delivered electrifying cover images, including an iconic photograph in 1981 of a naked John Lennon curled in a fetal position with Yoko Ono.

Music coverage in all of its forms — news, interviews, reviews — was the core of Rolling Stone, but its influence also stretched into pop culture, entertainment and politics. A bastion of liberal ideology, the magazine became a required stop for Democratic presidential candidates — Mr. Wenner has personally interviewed several, including Bill Clinton and Barack Obama — and it has pulled no punches in its appraisal of Republicans. In 2006, Rolling Stone suggested George W. Bush was the “worst president in history.” More recently, the magazine featured Justin Trudeau, the prime minister of Canada, on its cover with the headline, “Why Can’t He Be Our President?”

The magazine also published widely acclaimed political stories, including one in 2009 on Goldman Sachs by the writer Matt Taibbi, who famously described the company as “a great vampire squid wrapped around the face of humanity.” The next year, the magazine ran a piece with the headline, “The Runaway General,” that ended the career of Gen. Stanley A. McChrystal.

But that was perhaps the last Rolling Stone cover piece that gained significant journalistic acclaim. And the magazine’s reputation as a tastemaker for the music world had long since eroded, as Mr. Wenner clung to the past with covers that featured artists from his generation, even as younger artists emerged. Artists like Paul McCartney, Bruce Springsteen and Bob Dylan have continued to secure cover spots in recent years.

Rolling Stone suffered a devastating blow to its reputation when it retracted a debunked 2014 article about a gang rape at the University of Virginia. A damning report on the story by the Columbia Graduate School of Journalism cited fundamental journalistic failures. The article prompted three libel lawsuits against Rolling Stone, one of which led to a highly publicized trial last year that culminated with a federal jury awarding the plaintiff $3 million in damages.

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