“It’s a wonderful mess,” says Natalia Vodianova as she walks into the living room of her apartment in Paris, the Eiffel Tower looming outside the window. A polished Yamaha baby grand is surrounded on all sides by a candy-colored assortment of kids’ stuff: wooden puzzles, a Playmobil castle, a rocking horse, and a plastic cash register and toy telephone for junior wheeling and dealing. They blend in with more-adult amusements, including a roulette wheel set into a Louis Vuitton steamer trunk. On almost every surface there are stacks of books—Vodianova’s partner of six years and the father of her two youngest children, Antoine Arnault, doesn’t like to get rid of any of them. Pop novels like The Maze Runner lie on top of poker manuals, next to not-quite-best-sellers, like a French guide on marketing to women. There are enough auction house catalogs and coffee table tomes (Yves Klein, Steve McCurry, Erwin Olaf, Alexander McQueen) to stock an art-book store—albeit one that doesn’t mind dust jackets stained with rings left by bottles of baby formula. Where there are no books, there are bucket-size Cire Trudon candles, vases upon vases of poppies and pink roses, and framed vacation snapshots of the Vodianova-Arnault clan. Were it not for the important artworks scattered throughout the apartment, there would be little to suggest that this is the home of one of the world’s most successful supermodels and the son of France’s premier luxury tycoon, Bernard Arnault.

Settling onto a sectional sofa near the piano, Vodianova juggles her children, briefly handing Roman,1 year old, off to Lucas, who is almost 16, while Viktor, 9, plinks away on the piano. Curly-headed Maxim, 3, tugs at his very patient 11-year-old sister Neva’s long, white-blonde hair. Vodianova moved into the duplex five years ago with Arnault and her tribe, which then comprised just the three oldest children, fathered by her ex-husband, Justin Portman. Enough time has passed for tiny hands to have smudged their fingerprints onto the apartment’s pale walls, the Portman branch to have added French to their Russian and English, and the china closet to have been transformed into a small pharmacy. (This group goes through a lot of Band-Aids.) Upstairs, the wall next to Roman’s room is filled with handwritten measurements tracking the heights of the kids, as well as those of their mother and grandmother, Bernard Arnault’s first wife, Anne Dewavrin (here called “Mamoune”), and family friend Karlie Kloss, who is taller than everyone, except Antoine. “We need more space,” says Vodianova, who yearns for at least one room that isn’t “infested with toys,” adding, “We’re looking, but I’m almost paranoid to let this place go. We’ve been so happy here.”

Quietly handsome, with a deep voice and his father’s reserve, Arnault was childless when he and Vodianova started seeing each other in 2011, around the time she and Portman were divorcing. “Since almost our first date, it has been a superb roller coaster ride,” he says. For both of them, it was a case of when you know, you know, though Arnault knew first. “Natalia doesn’t even remember it,” he recalls of the first time they met, on a shoot for a 2008 Louis ­Vuitton campaign (he was then the house’s head of communications). It featured a supermodel cast of Vodianova, Eva Herzigova, Angela ­Lindvall, ­Claudia Schiffer, Naomi Campbell, and Stephanie Seymour. “I remember ­seeing her and my jaw sort of dropping internally,” Arnault says. “I mean, of course she’s beautiful, but she has something undefinable: her look, her air; there’s an aura around her.” Afterward, whenever they bumped into each other over the next few years or showed up at the same group dinners, they were friendly. Finally, after Arnault had broken up with his girlfriend, “and I’d read she’d split from her husband,” he says, “I texted her.” Vodianova held him off for months before agreeing to meet at his apartment, to avoid a chance sighting and igniting media speculation. “We had a drink on his terrace with a view of Paris,” she says, “and it was completely ridiculous. We were both super shy. I knew that seeing him in jeans, like a casual, normal guy, I liked him. But he didn’t even try to kiss me! I’m not the kind of girl who worries if a man likes her. I mean, somewhere deep down I’m really fragile, and it would hurt me, but I put on a lot of bravado, even to myself. So I thought, OK, maybe he just wants to be friends?” Subsequent texts disabused her of the notion.

It was the next date, a dinner at La Société, in Saint-Germain, when Vodianova fell for him. They found out they were renting summer houses 10 minutes away from each other on Ibiza. Vodianova hadn’t introduced her children to anyone since her divorce, and though things were just taking off between them, she invited Arnault to drop by. “Not only were the children there,” Arnault recalls, “but also her grandparents, her mom, and a couple who were taking care of the kids. At some point, the woman in the couple had a panic attack, and we had to call an ambulance. So I knew what I was getting into. Very quickly after that I was going almost every weekend to ­England, where she was living. I told her, ‘Come to Paris, I want us to live together.’ She said, ‘You realize it’s not just me, right?’ But she thought about it, negotiated a bit with her ex-husband, who lives in Uruguay, and that was that.” That fall, the kids started at an international school in Paris. “I told her that I wanted to have children with her,” Arnault says. It didn’t take long, though Vodianova hesitated at first. “I mean, I already had three gorgeous children,” she recalls. “Maybe initially I was doing it more for him than myself, but, at the same time, when you’re in love with a man, you want to reproduce him as many times as possible.” Maxim came two years later, and two years after that, Roman was born.

“Going from zero to five kids in two and a half years is the most wonderful thing in the world,” Arnault says. “Not only having our own, but her kids as well. Natalia is much more mature as a mother than she was when she had her first babies. And it’s a bit selfish, but the older ones are a great help with the little ones!” At about the same time that his new family arrived, Arnault assumed the role of CEO of the men’s wear label Berluti and, six months before the birth of Maxim, he took on the position of chairman at the Italian cashmere company Loro Piana. The domestic and professional changes have been mutually supportive, he says, making him a better communicator.

Those of us with long fashion memories still might find it hard to reconcile the 17-year-old Vodianova, whose sensuality was so smolderingly nymphet-like that it was almost troubling, with the 35-year-old woman she is today. But even now, in photos Vodianova can still linger in that same indeterminate space between girlhood and womanhood. When the photographer Patrick Demarchelier was lining up a shot with Vodianova and her children for this story, she authoritatively commanded, in Russian, that her brood settle down. A second later, she smiled and turned her head up toward Demarchelier, making limpid eye contact with the camera, casting her spell.

Vodianova’s well-known backstory, which she’s neither concealed nor romanticized, makes the tangled innocence she brings to a picture especially compelling. Raised by a single mother, she grew up poor in the then-Soviet city of Gorky, now Nizhny Novgorod, caring for her disabled younger sister, Oksana, who suffers from cerebral palsy, and selling fruit with her mom at age 11. Her grandmother, a retired factory worker who enjoyed “polar bear swims” in icy waters, gave her a measure of stability and comfort—as well as a sense of style. “She had this red hair she put in a 1940s chignon, and wore red lipstick every morning,” Vodianova remembers. At 17, Vodianova was scouted—“If I hadn’t become a model I would probably have ended up living on the street,” she says—and went to Paris, where she rose so precipitously she earned the nickname Supernova. At 19, already a catwalk and cover star and just married to Portman, she gave birth to Lucas, causing fashion insiders to wonder if, given the immense wealth of her husband’s real estate family, she might just retire.

The answer came six weeks after Vodianova gave birth, when she opened the Yves Saint Laurent show. “I hadn’t been Westernized yet when I fell madly in love and became pregnant,” she recalls. “Where I come from, it was normal to have a baby at 19. Maybe most of the Western girls brought up with a family that was strong for them would say, ‘You’re very precious, are you sure about this guy?’ No one told me I was precious in that sense, so love, for me, was that precious thing. It made sense to me completely. Would I recommend the same thing to my daughter today? Absolutely not.” Even now, despite all her professional and personal accomplishments, she remains “vigilant,” she says. “I never feel secure. I’m always prepared for the worst!”

Vodianova’s immediate family may not have been able to give her much materially, but they certainly gave her a sense of purpose. Her famously strong work ethic remains unabated, even if her priorities have shifted. She allocates about one month a year to editorial work and fulfilling contracts for Calvin Klein and Guerlain. Other than that, she spends her days—until 4 p.m., when the kids come home—at the Paris branch of the Naked Heart Foundation, which is located in a massive modern office building a few blocks from her apartment. (There are offices in London and Russia too.) Though the foundation, which Vodianova started in 2004, throws two glamorous galas every year, the Love Ball and the Fabulous Fund Fair, and participates in several other annual art and fashion events, at the office her look is no makeup, distressed jeans, and Louis Vuitton combat boots. Her grandmother, who still gives her beauty tips, likely would not approve.

Naked Heart came into being after a siege at a primary school in Beslan, North Ossetia, by Chechen separatists in 2004 pushed Vodianova to do something for her country. Her idea was to build playgrounds in rough areas in Russia, adapted for kids with special needs like her sister. Vodianova explains that there is a grave lack of institutional and social support in Russia, which leads many families to place children with autism, Down syndrome, or cerebral palsy in state-run orphanages. “My mom kept Oksana in the family, which was an exception, and I saw how tough it was for her to raise her,” she says. To date, Naked Heart has built 177 playgrounds in Russia, the U.K., and Peru, with at least 17 more approved for 2017.

Eight years after Naked Heart was born, “we were building as much as we could in Russia and wanted a bigger challenge,” says Vodianova. Assembling a group of experts, the foundation designed a model family support center for people with special needs, which opened in Nizhny Novgorod in 2011, and which Oksana attends. Next, Naked Heart developed a mobile teacher-training program for children with autism, with a focus on early intervention, that is now active in 10 schools and 24 preschools in Russia. Since 2012, the foundation has put on an annual educational roundtable in Russia, and donates to other NGOs with complementary missions. In 2015, Vodianova became a board member of the Special Olympics, and she isn’t shy about using her fame to try to change the conversation culturally. When the Russian pop star Dima Bilan asked her to appear in one of his videos, she agreed under the condition that he let her write the script. “Ne Molci,” which translates to “Don’t be silent,” is a Cinderella story about a woman sure she won’t find love because of her daughter’s Down syndrome. The video, in which Vodianova makes an appearance, has had more than 7 million views on YouTube.

Vodianova’s current obsession is Elbi, the micro-giving social network app she developed two years ago with her media advisor, Timon Afinsky, which is currently in beta and will relaunch after testing. Elbi encourages users to share original artwork and photos to send messages of support to kids in need; each time fellow users like your content, they donate $1—the maximum amount allowed—to the linked charity. “We want to make giving easy, something you can do sitting around at the airport, without a second thought,” Vodianova says. She has already participated in several international philanthropic conferences, and she plans to ramp up those appearances. (She just signed with the Kruger Cowne agency, which also represents Sir Bob Geldof, Archbishop Desmond Tutu, and Elle Macpherson, to help her “make more educated decisions” about how to make a bigger impact.) As a public speaker, Vodianova is heartfelt and emphatic. In the future, it’s more likely that we’ll be seeing her pacing a stage wearing a headset mike rather than striding down the runway. Either way, it will be extremely hard not to give her our full attention.

Watch: Natalia Vodianova Stars in Bruce Weber's New Home Video