“Who comes next?”

That’s the one question luxury insiders and fashion lovers have about the biggest company in the industry, LVMH.

The Paris-based behemoth has only ever been led by founder and CEO Bernard Arnault, the 75-year-old patriarch, who’s also one of the wealthiest people in the world (he briefly topped the rich list last year).

Given LVMH’s clout as one of Europe’s most valuable companies and the owner of some of the most loved luxury brands, everyone—from investors to shoppers—is interested in the company’s future.

Arnault’s children are involved in the family business, and most are part of the LVMH board too. That has prompted parallels to the TV show Succession and theories on who might take the reins from him.

But it will be a while before there are any definite answers, because Arnault doesn’t plan to retire. And even though the LVMH chief is aware of the speculation surrounding his future successor, he says the jury is still out.

“I have five members of the family working in the group. Let’s see if one of them can take over,” Arnault told Bloomberg in an interview published this summer.

As founder-CEOs often do, Arnault sees LVMH as his baby. He spends 12-hour days managing the company he turned into a global conglomerate with €86.2 billion ($92.17 billion) in revenue last year.

The luxury chief made LVMH’s board extend the retirement age for its chairman and CEO (i.e., himself) from 75 to 80 just so he could stay longer. After that, Arnault received a letter from Warren Buffett, then 93, the legendary investor and founder of Berkshire Hathaway, warning him it was a mistake because it was too low an age limit, Bloomberg reported.

Lining up the heirs

The future is inevitable—as is the eventual succession at LVMH.

The company has been shaking up its top leadership, including hiring former Danone CFO Cecile Cabanis as the next in line to longtime CFO Jean-Jacques Guiony.

However, the Arnault family still holds a tight grip on LVMH, with roughly 64% of the company’s voting rights and 48% share ownership. The structure of the conglomerate’s holdings company, Agache, was changed to resemble a limited partnership that gives more power to even small stakeholders.

Second-generation Arnaults have also been stepping up the ranks to play pivotal roles at the company for years.

Delphine, 49, is the chair and CEO of Christian Dior Couture, part of LVMH’s most lucrative business segment, which covers fashion and leather goods.

Antoine, 47, is the conglomerate’s image and environment director who was instrumental in LVMH inking an Olympics partnership.

Alexandre, 32, is the executive vice president of jewelry brand Tiffany & Co.

Frédéric, 29, leads LVMH’s watch brands, including Tag Heuer and Hublot, where the youngest of the siblings, Jean, 25, is a director.

Besides Jean, four of the five children sit on LVMH’s board.

LVMH’s succession might be shrouded in mystery, but we know the players and the stakes in deciding who takes the mantle from Arnault. The patriarch is in no rush to leave, so we’ll just have to wait and watch.