HBO's 'The Leftovers' begs the question: What on Earth?

What has happened to the world?

The question can be asked generally, but it has a more specific application in the case of “The Leftovers,” HBO's series adaptation of Tom Perrotta's novel about the aftermath of the so-called Sudden Departure, a possible Rapture that has taken 2 percent of the population — or 140 million people — from the planet. Developed for television by executive producers Perrotta and Damon Lindelof (“Lost”), the drama premieres Sunday, June 29.

Also an executive producer of the show, Peter Berg (“Friday Night Lights”) directed the pilot. It introduces the fictional town of Mapleton, N.Y., where police chief Kevin Garvey (played by Justin Theroux) worries about his children (Margaret Qualley, Chris Zylka) while also maintaining concerns about the cultish and literally silent Guilty Remnant, a group that preys upon the remaining residents who search for meaning and a return to normalcy. Actually, make that “relative normalcy.”

Amy Brenneman, Liv Tyler, Christopher Eccleston, Carrie Coon, Amanda Warren, Ann Dowd and Michael Gaston are other members of the ensemble cast of “The Leftovers.” Perrotta says he appreciates the series' “interesting, and deeper, take” on his book.

“The great thing about TV is that it affords the writer an opportunity to be involved on the production end, and to have an ongoing involvement in the show,” Perrotta said. “Usually, once the script is written your job is done. Before long, we're going to move beyond the confines of the book, and then we're creating something new.”

After movies including “Armageddon,” “That Thing You Do!” and the “Lord of the Rings” trilogy, Tyler makes her series debut in “The Leftovers.” She says she's been happy to help keep a sense of mystery about the show, to the degree that when she shows up for work, “I usually just get in the van and don't even ask where we're going. It's usually 25 to 45 minutes outside the city (New York), and it's always different. Which is strange, because you'd think there is one town that is the town of Mapleton.”

“The Leftovers” is such a unique TV venture, Tyler notes that fact has heightened her adjustment to doing series television. “When you watch all the shows, you think it's just like making a movie — the episodes are like little mini-movies — but the truth is that it's really quite different. I suppose the hardest thing is accepting being comfortable with the unknown, because we're always waiting for the next script to see what's going to happen to our characters.

“I didn't realize what a control freak I am,” Tyler adds with a laugh. “I consider myself ‘quietly organized' in my own little weird way, but I'm also pretty relaxed and spontaneous. I'm adaptable, but we started filming this in the dead of winter, and it was just really cold. And it was this strange feeling of not knowing what we were doing, ever. Now it's a few months in, and our characters are starting to flourish, and we're like a family.”

Tyler's Meg gets Brenneman's wordless Laurie as her guide into the Guilty Remnant. For the typically lively veteran of such other shows as “NYPD Blue” and “Private Practice,” conveying thoughts and emotions without speaking is a fresh challenge.

“When I met with Damon Lindelof about a year ago,” Brenneman recalls. “He said. ‘OK, here's why you shouldn't take this job.' I said, ‘OK, lay it on me.' He said, ‘You don't wear any makeup, you don't talk, and it shoots in New York.' (The actress resides in California.) And I was like, ‘All right. I'm in.'”

Though he hasn't had a hand in writing all the “Leftovers” episodes, Perrotta likes the quality control his executive-producer role affords him even when his name isn't on a script.

“One of the things that has appealed to me about TV,” he reasons, “as it's come to be defined in the past decade or so, is the fact that audiences are just so interested in living with characters over long periods. Those become very powerful relationships. Even the novel doesn't have that kind of staying power.”

“The Leftovers”

Premieres at 9 p.m. Sunday, June 29, on HBO