Photo: Cass Bird. Styling by Heidi Bivens at The Wall Group; Hair by Tommy Buckett for Garnier Fructis at The Magnet Agency; Makeup by Hung Vanngo for CK One Color Cosmetics at The Wall Group; Special thanks to the Greenwich Hotel. Denim overalls from What Goes Around Comes Around. Photo: Cass Bird/New York Magazine

When Mad Men, AMC’s 1960s advertising drama, began, probably the only person who knew the clueless secretary with the unflattering bangs would become the show’s hero was its creator, Matt Weiner. The first episode was Peggy Olson’s first day on the job, her ears sticking out, her clothes ill-fitting, her ambitions un­formed. But with each season, Mad Men’s own girl Friday has ascended the corporate ladder, gaining power, sophistication, and better haircuts, only to arrive at the end of last season in her mentor Don Draper’s chair, finally wearing the literal (houndstooth) pants.

“In the opening credits, my name is after Jon Hamm’s, who stars as Draper,” recalls Elisabeth Moss, the 31-year-old actress who plays Peggy. “But when I did the pilot I was not necessarily in that position. I’m No. 4 on the call sheet. But Matt put me second in the credits. I guess he knew what was going to happen.” Don may be the show’s dashing face, but Peggy has always been its point-of-view character, “our Virgil,” in the words of Hamm, “leading us through this hellscape of ’60s advertising.”

When the show returns for the first half of its seventh and final season on April 13, it will be as much Peggy’s story as Don’s. Don is caught up in his past, his power and pull dissipating in a radically diversifying world—a man adrift in a future full of Peggy Olsons. As Peggy has spiffed up and risen, again and again, to the ­occasion, so has Moss, who has been nominated for an Emmy for playing Peggy four times, and on the strength of her skill turned a show about a suave, tortured anti-hero into one just as much about an earnest, driven heroine, a broadening of focus not incidental to Mad Men’s well-deserved reputation as one of the best dramas on television. When season five ended with Peggy going to another advertising agency, the panic among fans was such that Weiner, who guards secrets as zealously as the NSA—and more effectively—issued a spoiler of his own, promising Peggy would be back.

As we, the audience, are preparing for a post–Mad Men age, so is Moss, and she’s much further along than we are, having already embarked on a series of Peggy-less ­projects. Last year, she starred in Top of the Lake, Jane Campion’s idiosyncratic mini-series in which she played a troubled New Zealand cop. The two small films she made during the Mad Men hiatus—The One I Love, a mumblecore thriller with Mark Duplass, and Listen Up Philip, in which she plays a Brooklyn photographer in the midst of a breakup with a difficult author played by Jason Schwartzman—both made it to Sundance; the former was purchased by the Weinstein’s Radius-TWC.*

Photo: Cass Bird. Black tank dress from BASE Range; Rings by Jennifer Fisher and Svelte Metals; Safety pin earring by Loren Stewart; Necklace by Inez & Vinoodh. Photo: Cass Bird /New York Magazine

For the time being, Moss, who goes by Lizzie, is still most closely associated with Peggy, so much so that strangers often tell her how much the character inspired them to change jobs. TV has many ambitious women, but Peggy stands out among them for navigating a working world—with glass ceilings, boys’ clubs, and take-me-seriously work clothes—that feels, despite its period detail, remarkably contemporary. Peggy is “the one we relate to, the one that’s us,” Moss says, and the legions of essays and blog posts and tweets celebrating her extraordinary ability to lean in are proof of her connection to the audience. (Peggy Olson is easily the most GIF-ed feminist icon of all time.)

But as Mad Men’s fans continue to produce both Peggy Olson scholarship and Peggy Olson mash notes, Moss herself has a much less heady relationship to the character. “I don’t actually work in advertising in the ’60s. I’m an actor,” she says, laughing. “I’m just a normal person who worries and stresses about stupid shit. I like to sleep in. I like sushi. I love what I do. I think acting is super-fun. I don’t think it’s something super-serious.”

“Peggy has a sense of humor about things,” Weiner says. “But she is not as much fun as Lizzie is.”

Recently, at work, Moss asked her colleagues, “Do you remember when I used to come in and bring you assholes drinks and leave and that was my job?”

Having met Moss a handful of times through a close mutual friend, I knew better than to expect Peggy Olson to march into the ­nondescript but excellent sushi restaurant on Sunset Boulevard, where Moss goes so regularly the staff knows not to serve her shellfish with a face. But even I giggle-gasped to hear her say so self-­deprecatingly, “Acting is not stupid, but it’s a very strange profession, honestly. My job is to get up, and get dressed in someone else’s clothes, and go and pretend that I’m someone else. Who does that? Nobody does that. Strippers and actors do that.”

Despite her irreverence, what Moss excels at, as Weiner says, is “radiating reality. And of course that’s an act.” Whether she plays a copywriter or the president’s daughter, as she did for years on The West Wing, her performances have a satisfying, round-peg-in-a-round-hole, sweet-spot thwock of recognition. Hamm describes it as “an approachable, familiar aspect. Elisabeth’s characters and Elisabeth’s personality present themselves”—there it is again—“as one of us.”

The women she often plays can be pushed, but only so far: Don had to toss money in Peggy’s face just once for her to finally get a new gig. (Coincidentally, two of Moss’s other characters stabbed men in the guts last year.) “She has the ability to be stoic and flibbertigibbet, strong and mentally vulnerable,” says Duplass. And she can flip these skills on and off like a switch. When I ask if she ever takes her work and its attendant heavy emotions home with her, she says, “No, not at all. I’m the worst. I barely hang on to it while we’re filming. I am totally that person that they yell ‘Cut’ and I’m making jokes and doing stupid stuff. It’s fake to me to be any other way.”

“She’s not one of those actresses who is walking around with her headphones listening to Nine Inch Nails to get into a scene,” says Duplass. “She’s joking around casually and then you yell ‘Action’ and her heartbeat goes to 150 beats per minute.” The heart rate may be an exaggeration, but the massive spike is not: On The One I Love, her mike had to be changed and moved so it wouldn’t pick up its sound.

If Moss’s serious-minded characters are squarely at odds with her own, less serious personality, they all share a certain groundedness. She is not particularly hung up on celebrity. She thinks of herself as a regular person—which must relate to her ability to appear on-­camera like one. But it’s hard to stay normal when you’re even a little famous. It requires a kind of double ­consciousness: Moss asks photographers not to take pictures of her while she’s smoking, but when she sees paparazzi photos of herself leaving a restaurant, she thinks, That’s so weird. They must’ve had no one else to photograph that night. At the Golden Globes, where she ended up winning for her role in Top of the Lake, she was seated at a table with Megan Mullally, Mike Tyson, and Helen Mirren. (“Very ­normal, every other Sunday,” she jokes.) When she caught Mirren’s eye, she introduced herself. Mirren’s perfectly Helen Mirren–ish reply: “I know who the fuck you are.”

Moss does what she can to minimize these discontinuities, shielding herself from the vertigo of fame by collapsing her world into an extremely cozy radius. She rents an apartment in West Hollywood, newly home to two cats named Ethel and Lucy, and rents another one in lower Manhattan. When she’s in New York, she rarely leaves a few blocks in the East Village. When she’s in L.A., she revisits the same places over and over again. (At the restaurants and hotel bars we went to, she was greeted with the intimacy of a regular, the well-being of her family inquired after.) She is very close with her mother and brother, who is 18 months younger. She doesn’t particularly enjoy large parties, preferring to hang out at work or have dinners or small gatherings with friends, most of whom are or were her colleagues. She travels with a stuffed animal. She goes to bed late and sleeps later, if work doesn’t interfere. She watches lots of TV—Scandal, Parenthood, Nashville, The Good Wife, her Instagram handle references a Real Housewife—and wound down every evening while shooting Top of the Lake by binge-watching The Sopranos. As much as she can, she keeps things simple. When a huge moth flew into her bedroom and landed on a copy of J. K. Rowling’s The Casual Vacancy, Moss just tossed both out the window.

While she is filming Mad Men, Moss spends time on set even after she’s done with her own work. The cast is very close: “It’s not a real workplace” is how she puts it. “Base camp,” the area by the hair, makeup, and actors’ trailers, has been tricked out with a deck that has a roof, couches, and a fire pit, and the cast spends time there, lately playing Heads Up!, an iPhone game. Moss is the official president of base camp (Hamm is the “sergeant-at-arms”), and she has gotten extremely good at Hey Mr. DJ, a Heads Up! category in which the name of a song pops up on the iPhone screen and all the assembled players have to hum it, vocalize it, whatever, so long as they don’t use the lyrics, while the person holding the phone tries to guess the title.

She recently spent a Thursday night on set polishing her lyricless rendition of Pink’s “Just Give Me a Reason,” and the next night, at the Sunset Tower Hotel in Hollywood, she asked her table, “Are we really going to escape tonight without playing Heads Up!?” Seconds later, she had successfully turned the hotel patio into a living room, nine of her friends loudly humming “Respect” and “Man in the Mirror,” as Jessica Alba, Rachel Zoe, Kate Hudson, and Nicole Richie ate inside the restaurant 200 yards away.

Moss picks me up in her car for a drive to the beach wearing “beach clothes,” a loud fluorescent-pink-and-green zip-up hoodie over a short-sleeved peasant blouse, jeans with holes in the knees, and flip-flops. (“That’s my favorite part of ­articles,” she says as I write down the particulars of her outfit. “I always want to know what they’re wearing. I want to know what Amy Adams wears to lunch.”) She does not often go to the beach, and she’s anxious about our trip there, familiar enough with the conventions of celebrity profiles­—in which reporter and subject do activities together—to have overthought it. “I’ve been stressing about this. I don’t do anything,” she says. “I don’t go to classes. I hate hiking. I don’t go to flea markets. I would like to do that stuff but I just don’t do that stuff. I was like, ‘I guess we’ll go to the beach, because that’s something I would do if I had time and wasn’t so lazy?’ ”

As we drive down Sunset, she tells me that she thinks it’s her history as a ballet dancer that’s responsible for this tendency to burrow. “I have a weird sequestering thing that happened,” Moss says. “As a dancer, you don’t know a lot about normal everyday life. You grow up in this little world of ballet, and I feel like that carried on into my adult life, where I have blinders on to a lot of stuff.” Moss began dancing when she was 5, shortly before she started acting. She was born in Los Angeles, her mother a harmonica player, her father a music manager, and she was raised in what she sheepishly describes as a very lax ­academic environment, with her parents putting a serious premium on the arts. Her first real role came in a before–Sandra Bullock–was–Sandra Bullock mini-series, and she later played Baby Louise in a TV version of Gypsy starring Bette Midler—Moss has been attracted to serious characters from the beginning. But between the ages of 11 and 14, she focused on ballet.

Photo: Cass Bird. Lurex knit tank dress by Sonia Rykiel. Photo: Cass Bird/New York Magazine

Then she filmed a Martin Landau movie called The Joyriders, the first where she “wasn’t just playing someone’s daughter.” She was so charmed by the whole experience, “not just acting but being a part of the crew and having the sense of community,” that she decided to focus on acting. She got her GED at 15. At 17, she read with Aaron Sorkin to land the recurring part of Zoey Bartlet on The West Wing. At 19, she moved out of her parents’ house and to New York to appear in a play and decided to stay, intermittently flying back to L.A. for work. She shot the pilot for Mad Men within a month of shooting her final episode of The West Wing. Even on Mad Men, at just 23, Moss stood out as a veteran: Weiner recalls having to film a close-up in an early episode—the one in which Peggy is tasked with selling vibrating underwear masquerading as a weight-loss aid—and saying to Moss, “I don’t know what I need here; I think I need a little bit more.” She asked him what lens he was on. “Now I joke to her, ‘Set your face on 7,’ ” Weiner says.

We are almost at the ocean when I bring up Scientology, the church Moss was raised in. Her affiliation with the church remains the strange, odd fact of her biography, the thing that does not belong in her regular-chick story. “I’m not going to talk about it anymore,” she says firmly. “I said what it meant to me, and anyone can go and look at that if they want to know what I feel. But now it’s private, off limits.”

She has previously spoken about how the church is personally helpful to her, not anti-gay, and “grossly misunderstood by the media.” But Moss does not talk about Scientology even with friends and seems very comfortable with how uncomfortable it makes other people. “I would feel the same way, honestly,” she says. “I think if there was something that I didn’t know and didn’t understand, I would probably feel as opinionated. You know how you’re opinionated about when someone breaks up? Celebrities break up and you just feel like you know what happened?”

She pulls up to a red light on the Pacific Coast Highway, the water sprawling in front of us. “I’m not sure if I should go left or right,” she says. We chatter for a few minutes about finding parking, and as we head into the lot, I note that the ocean conveniently interrupted my questions about Scientology. Moss does not miss a beat. “Exactly. Like, ‘Oh, there’s the ocean. Oops. Sorry, can’t. Look how pretty it is.’ ”

Moss does have a quick and impish streak, most recently on display on the Golden Globe red carpet when she flipped off the “Mani Cam” on live television. She didn’t do it out of spite so much as to see what would happen: She wasn’t sure whether the feed was live. She can be a little la-di-da naughty like this—not ­malicious, but casually willing to risk some trouble for the sake of fun. At the Sunset Tower, she swiped an ashtray, after some egging on, just because she’d been ­wanting to take one home.

In the parking lot, she grabs a hat and coat from the trunk of her car, which also contains nonperishable groceries from ­earlier in the week. It’s mid-February, and she has been working so much on Mad Men she still has not entirely unpacked from spending Christmas in Chicago with her extended family. We sit down and I circle back to her point about celebrity breakups: She was in one. Moss was briefly married to former Saturday Night Live cast member Fred Armisen, whom she met when Jon Hamm hosted the show. They were married a year later and broke up eight months after that, in 2010. Armisen has since described himself as a “terrible ­husband” on Howard Stern, a classification to which Moss nods in agreement.

Photo: Cass Bird Photo: Cass Bird/New York Magazine

“Looking back, I feel like I was really young, and at the time I didn’t think that I was that young,” Moss says. “It was extremely traumatic and awful and horrible. At the same time, it turned out for the best. I’m glad that I’m not there. I’m glad that it didn’t happen when I was 50. I’m glad I didn’t have kids. And I got that out of the way. Hopefully. Like, that’s probably not going to happen again.”

Their breakup made it into the tabloids, an eye-opening experience for her. “I always knew that the stuff that you read is not true, but when I was in the situation and you really, actually read things that you apparently said or did that are 100 percent made up … It’s just the strange, simple thing of, that’s your heart they’re talking about, and it just … it sucks,” she says. But this ­unpleasant brush with the tabloids has not stopped her from occasionally reading them. “I’m not perfect in that way,” she admits. “I enjoy a little gossip. I like looking at photos of celebrities going to Starbucks.”

As the end of Mad Men looms—in late March, she goes back to film the final seven episodes, though those won’t air until 2015—she’s as interested in working in film as in TV, because movies are less of a time commitment. And she’s not specifically looking to raise her profile. “Nobody, unless you’re an asshole, should sit around thinking, I want to be more famous and win more awards,” she says. “That’s a horrible person.” Even so, Moss finds herself with more pull, and more fame, than she’s ever had before. “I had to actually have that moment of observing that I have to read the whole script and decide whether or not I want to do this movie, because if I do it, the movie will get made, and if I don’t do it, the movie won’t get made,” she says. “That’s new.”

On the beach, her eyes extremely pale against the ocean, Moss remembers ­playing Catch Phrase not so long ago with the cast of The One I Love, and her own name came up as one of the answers. “It was the most exciting moment ever,” she says. Then she shrugs. “It’s come up four times since. Now they’re like, ‘You.’ And I’m like, ‘Elisabeth Moss.’ ”

*This article appeared in the March 10, 2014 issue of New York Magazine.

*A previous version of this article said The One I Love was purchased by the Weinsteins; it was purchased by their boutique label, Radius-TWC.