Of all the shows 20th Century Fox Television produces, it’s the animated ones that have taken on a life of their own.

“The two most profitable TV series the studio has ever done are ‘The Simpsons’ and ‘Family Guy,’ ” says 20th TV chairman and CEO Gary Newman, who joined the company in 1990, shortly after the yellow-skinned Springfield family branched off from “The Tracey Ullman Show” into its own animated sitcom, battling NBC’s top-rated “Cosby Show” to a near-draw in its second season. A decade later, he worked with Seth MacFarlane to adapt his animated short “Larry and Steve” into what would become “Family Guy.”

“I think what really stands out about those two series is both came from creators who had a very specific and strong vision, and in both cases, the people responsible for that vision have stayed in control of the show,” Newman says.

Twenty-five seasons into “The Simpsons” — a show so established that a good percentage of its audience isn’t old enough to remember a time when the series wasn’t on the air — executive producer James L. Brooks still attends every table read, while creator Matt Groening continues to serve as keeper of the brand, signing off on all ancillary and consumer-product opportunities.

As proof of the series’ continued popularity, Electronic Arts’ “The Simpsons: Tapped Out” app ranks as the top mobile game of the year, and Universal Studios Orlando expanded its Simpsons ride into a full-blown section of the park earlier this summer.

“Similarly, ‘Family Guy’ is just as much Seth’s baby,” Newman says.

Despite recent steps into the live-action world — which include helming last year’s hit “Ted,” and directing and starring in the 2014 oater “A Million Ways to Die in the West” — MacFarlane remained closely involved with not just “Family Guy” but two other Fox-produced shows as well: “American Dad” and “The Cleveland Show” (a “Family Guy” spinoff that ended its 88-episode run in May).

Along with Loren Bouchard’s “Bob’s Burgers,” these toons constitute Fox’s formidable “Animation Domination” programming block on Sunday nights. The production division, which Newman oversees with fellow chairman-CEO Dana Walden, also makes toons for other outlets, including “Brickleberry” for Comedy Central.

The process for creating TV animation has changed dramatically over 25 years, shortening what used to be a nine- to 15-month production cycle to only four to six months. In the past, if something important like an election was happening and “The Simpsons” writers wanted to riff off the current president, they’d have to include a “donut” in the show, leaving a hole in the animation that could be filled at the last minute. Now, thanks to the digital revolution, animated shows can be much more relevant.

“If you’re shooting a live-action multicam show, you can be on the air with it two weeks later, so it’s possible to be very current,” Newman says.

Despite the painstaking animation process, the toon format has always offered certain advantages over traditional sitcoms.

“At an obvious level, your cast doesn’t have to age like they do in live action,” Newman says. “(In live action,) 10 years in, those cute 7-year-old kids are now young adults. Bart Simpson is the same age he was when the show started, and Stewie’s going to be a young, precocious, insane baby for the duration of that series.”

One of the biggest changes in Newman and Walden’s job descriptions this year has been the addition of syndication and distribution duties, which sparked the announcement that “The Simpsons” will finally be headed to cable, once it finds the right partner.

“It just felt as if the show isn’t losing any of its creative steam,” Newman says. “Rather than continuing to wait until it goes off the air, we think it’s an enormous opportunity for whichever cable network decides to step up to it.”