When Kimmy escapes from the Reverend Richard Wayne Gary Wayne, she doesn’t look wrecked; her expression is pure sunshine. Illustration by David Saracino

The credit sequence for “Unbreakable Kimmy Schmidt” is a variation on a familiar viral meme: an excitable trailer-park resident gets interviewed on local TV, only to have his words Auto-Tuned into a catchy jingle. The witness describes a bizarre rescue: four women emerge from a concealed bunker where they’ve been held captive for years by the “weird old white dude” next door—the leader of a doomsday cult. “Unbreakable!” the resident shouts, waving his arms, flooded with emotion. “They alive, dammit. But females. Are strong as hell.”

At once crude and affecting (and impossible to get out of your head), the clip operates as shorthand for the show itself, the first post-“30 Rock” series to be produced by Tina Fey and Robert Carlock. Like its opening credits, “Kimmy Schmidt” is a peculiar, propulsive mashup of tabloid obsessions, a sitcom about one of the “Indiana mole women,” Kimmy Schmidt, who was kidnapped by the Reverend Richard Wayne Gary Wayne in eighth grade. She then endured—the show strongly implies—pretty much what you’d imagine. When Kimmy escapes, however, she doesn’t look wrecked: instead, her expression is pure sunshine, a toothy grin of astonishment and delight. In her intractable optimism, she shares something with another Indiana native, Leslie Knope, from “Parks and Recreation,” except that this is a Leslie Knope who has been to Hell.

In the first episode, Kimmy and her fellow-captives appear on the “Today” show, where they’re offered an “ambush makeover” and gift bags, then sent off with a cry of “Thank you, victims!” As the van heads out, Kimmy makes a run for it. Rather than go back to her home town, she decides, she’ll reinvent herself in Manhattan: she’ll get a job, an apartment, and a life in which no one sees her as damaged goods. She finds a batty landlady, played by Carol Kane, and an outrageous roommate, Titus Andromedon (played by Tituss Burgess, who played D’Fwan on “30 Rock” ’s “Real Housewives” parody, “Queen of Jordan”); she also finds a boss, Jacqueline Voorhees (Jane Krakowski), an Upper East Side trophy wife, whom Kimmy initially mistakes for another captive—because, after a face peel, Jacqueline isn’t allowed to step outside her gated town house. “Is that your reverend?” Kimmy asks, seeing a portrait of Jacqueline’s husband. “Did he peel your face? Do you need help?” She does need help, actually: Kimmy becomes her assistant.

Fey and Carlock sold the show to NBC, under the title “Tooken,” but the network eventually passed—at which point Netflix stepped in, committing to two seasons. In the context of cable comedy, “Kimmy Schmidt” is a very odd bird. Plenty of ambitious series do dark material, but they match their insides to their outsides: they’re dramedies, like “Getting On,” or indie-inflected auteurist shows, like “Louie” and “Girls”; sometimes they’re caustic satires, in the tradition of the original British version of “The Office.” “Kimmy Schmidt,” on the other hand, is network bright. It’s all neon pink and Peeps yellow, energized by the Muppet-like intensity of Ellie Kemper’s performance as Kimmy and packed, like “30 Rock,” with surreal zingers. At times, it resembles a Nickelodeon tween show—which is just how its heroine might imagine her own life. Yet, without any contradiction, it’s also a sitcom about a rape survivor.

The show doesn’t address sexual violence head on; it’s possible to watch without dwelling on the details. But Kimmy’s ugly history comes through, in inference and in sly, unsettling jokes about trauma, jagged bits that puncture what is a colorful fish-out-of-water comedy. The backstory that emerges combines elements from a number of familiar tabloid stories: those of Katie Beers (abducted from her abusive family, kept in an underground bunker), Elizabeth Smart (snatched from her bedroom by a self-styled messiah), Jaycee Dugard (abducted from her front yard), and the three women who were rescued two years ago in Cleveland, after having been beaten and raped for years by Ariel Castro. At times, the story feels inspired by Michelle Knight, one of Castro’s victims, who wrote a memoir called “Finding Me.” Like Kimmy, Knight had no family to go back to; her upbringing was a horror. But, to judge from newspaper profiles, she has not merely survived the abuse—she’s resilient and downright giggly, a fan of karaoke and dancing, angels and affirmations. It’s a powerfully girlish model of human toughness.

Kimmy’s vision of the good life has exactly that vibe: she wants to enjoy what she’s missed out on. Roaming around New York, she binges on candy, like a crazed toddler. She buys sparkly sneakers. Peppy and curious to the point of naïveté, she acts as if she’d learned about life from sitcoms—she gets into a love triangle, she goes back to school, she’s eager for every party. But there’s also something tense and over-chipper about Kimmy’s zest, an artificial quality that even the cartoonish characters around her can sense is “off.” Yes, there was “weird sex stuff” in the bunker, she blurts out to her roommate. She has an unexplained Velcro phobia. At night, she wakes up from a fugue state and finds herself rinsing off a knife in the shower or attacking her roommate. (“This isn’t the Chinatown bus!” Titus tells her. “You can’t just choke people who are sleeping.”) When Kimmy decides to take things to “the next level” with her new boyfriend, she mashes his face with the heel of her palm and tries to overpower him. She marvels, “All the stuff I thought I knew was way wrong.”

This is rare material for a sitcom. But it’s not unusual for modern television, which has been experiencing an uptick in stories about sexual violence—a subject once reserved for Lifetime and “Law & Order.” Here’s a partial list of dramas in which at least one central character has been raped: “Game of Thrones,” “House of Cards,” “Mad Men,” “American Horror Story,” “Outlander,” “The Americans,” “The Fall,” “The Fosters,” “Scandal,” “Top of the Lake,” “How to Get Away with Murder,” and “Switched at Birth.” You could call this a copycat phenomenon, but I’d argue that better roles for actresses made it happen: when women’s lives are taken seriously, sexual violence is going to be part of the drama.

For some critics, these recurrent rape stories seem cheap and exploitative—a way to show violent sex in the guise of social commentary or, in other cases, to insert a sad backstory to justify a woman’s harshness. There are definitely examples of this: a scene on “Game of Thrones” last season in which an evil brother overpowered his evil sister (who was also his evil lover—this is “Game of Thrones” we’re talking about) was so incoherently conceived that it couldn’t separate kink from assault. But what’s striking is that most such plots, in genres from camp melodrama to domestic fiction, are skillfully handled. Well-drawn characters like Mellie Grant, on “Scandal,” Elizabeth Jennings, on “The Americans,” and Callie Jacob, on “The Fosters,” may be rape survivors, but that’s not where their stories stop. They’re more than their worst day.

In Kimmy’s sparkliest dreams, that’s how she hopes the world will see her, too. Like many newbie sitcoms, “Kimmy Schmidt” stumbles, at times, to find its tone—and, with thirteen episodes launched at once, it doesn’t have the freedom to rejigger itself. A few characters flop, such as Kimmy’s Gomer Pyle-ish stepdad. While jokes about race were a strength of “30 Rock,” in “Kimmy Schmidt” they have a lower hit rate. Titus, an effervescently gay, black failed actor from Mississippi, pulls off every daring gag. (He also gets the best subplots, including a truly silly music video called “Pinot Noir,” meaning “black penis.”) But Kimmy’s Vietnamese boyfriend, Dong, is bland, and one of her fellow-hostages, a Latina maid, is a cipher. As Arthur Chu wrote in a sharp essay for Slate, the problem isn’t that the show’s hackier ethnic jokes are rude; it’s that they’re not rude enough—they don’t explode stereotypes with real daring and specificity.