So Graydon is gone. Now what?

The coming departure of Graydon Carter, Vanity Fair’s editor for 25 years, has set off a race to inherit his throne. Rarely does such a coveted editorship come up for grabs, even in an industry undergoing an unusual amount of churn. As executives at Condé Nast consider their options, editors and people in the magazine world say the winning candidate has to check off a few boxes:

1. Be comfortable in Vanity Fair’s swirling spheres of celebrity, politics, journalism and finance. Mr. Carter hosted parties and owned trendy restaurants. Mingling, and finessing a seating chart, are key.

2. Be willing to navigate the tumult at Condé Nast, which in the past year has shaken up top leadership and reorganized its production structure as it weathers an industry-wide financial downturn.

3. Embracing the digital future is a must. So is the ability to generate new revenue streams to offset continued declines in print advertising and circulation.

4. Impress Anna Wintour, the Vogue editor who now does double duty as Condé Nast’s artistic director. Ms. Wintour will likely want an ally at Vanity Fair, one of the company’s biggest titles, as she expands her power and influence.