It smells like teen spirit.

The babydoll dress that turned Anna Sui into a fashion superstar unleashes a flood of memories about the early days of grunge — when Nirvana ruled the airwaves and the original supermodel squad (Naomi, Linda, Christy) helped turn a short, frilly frock into a fashion icon.

That original dress, along with 100 or so other looks from the American designer, are featured in the bright new exhibit, “The World of Anna Sui” at the Museum of Arts and Design.

“There’s so much history and passion in this collection,” Sui tells The Post. “I held on to all of my archives, so it’s really a complete display. We’ve basically kept a museum in our New York office.”

Back in the late ’80s and early ’90s, Sui was working as a stylist and running with the celebrity fashion crowd. By then, she was designing her own clothes, but had yet to hold her own runway show.

“Just to get the confidence to put my own designs out there was tough for me, but Linda [Evangelista] discovered a few of my dresses during a fitting,” Sui says. “After she wore the dress to a couture show, I started getting phone calls from everyone. Karl Lagerfeld was like, ‘Who’s this Anna everyone’s wearing?’ ”

It was around this time that Sui got the push she needed. She was in Paris for the couture shows with her friend Steven Meisel, and while on their way to the Jean Paul Gaultier show, they stopped to pick up Madonna at the Ritz (as one does, of course).

“[Madonna] had racks and racks from every designer in Paris. Christian Lacroix, Chanel . . . I was so jealous!” Sui says. “She came out in a Gaultier coat and when she took off her coat, she was wearing my babydoll dress in black. I gasped.”

Now, nearly 30 years later, Sui has more than 50 boutiques around the world and her clothes are sold in hundreds of stores. Her looks are head-to-toe stories — grunge, Mod, Hawaiian, hippie, cowgirl — and they still inspire: You can walk into any store and find a slew of Sui-esque ’90s throwbacks.

The idea for the museum show started in London several years ago, when Sui saw an exhibit of the legendary designer Thea Porter’s work at the Fashion and Textile Museum. She and the curator started talking, which led to a meal and the first iteration of Sui’s exhibit, which opened at the London museum in the summer of 2017.

Sui, a longtime West Village resident, is happy to see her designs displayed in the city where they started.

“It was a much different New York when I was starting out, but that’s what is so great about having the exhibit here,” she says. “I lived here most of my life. I came to Parsons and never left. All of my workers, patternmakers and [seamstresses] past and present, are here. It’s really special.”

“The World of Anna Sui” runs through Feb. 23 at the Museum of Arts and Design, 2 Columbus Circle