In a city that hasn’t been known for its late-night dining options, Chinatown has long been an after-hours destination. Now restaurants in other neighborhoods — even places that serve Western fare during regular hours — are introducing their own late-night menus featuring dishes inspired by Asia.

At Sel de la Terre, a French restaurant in the Back Bay, the kitchen looks toward Korea Tuesdays through Saturdays after 10 p.m. Its Late Night Seoul Kitchen menu offers dishes such as Korean-style fried chicken, steamed buns, and noodle soups.

In the Theatre District, W Boston restaurant Market offers a special menu on Fridays and Saturdays from 10 to midnight. The salmon sashimi, chicken samosas, and mushroom eggrolls cost $10 per plate. And a pop-up restaurant called Guchi’s Midnight Ramen has been a smash, taking over local establishments such as the Gallows and JM Curley for a few nights at a time, selling out tickets in minutes flat.

If European cuisine still rules Boston’s upscale restaurants, Asian food is increasingly influential. Customers are gravitating to its bright, bold, and spicy flavors, and chefs see such late-night menus as a way to bring in crowds. The National Restaurant Association study “What’s Hot in 2012” predicts the rise. Surveying nearly 1,800 chefs, it names street-food-inspired appetizers and main courses, fusion cuisine, Southeast Asian and Korean cuisine, Asian noodles, small plates, Asian-flavored cocktails, and more as trends for the year.

For diners today, value is paramount. The often lower price point of small plates and Asian fare is attractive, particularly when it comes to late-night snacking.

“A French restaurant is going to be very expensive, and people don’t want to spend another $60 or $70 late at night,” says chef Jiho Kim, who helped create the Late Night Seoul Kitchen menu at Sel de la Terre. “People go and spend $10.”

These menus also make sense for the restaurants that offer them, filling seats during what might otherwise be slower times. Market, for example, has seen a spike in late-night traffic since introducing its version at the end of July, says chef de cuisine Brian Anderson. The weekend of July 27, numbers were up 77 percent from the previous year; the following weekend they were up 197 percent.

Market has particularly focused on bringing in restaurant-industry workers, who keep late hours, Anderson says.

“We have seen some great business pick up late night,” he says. “People are drawn to Asian-inspired food. Personally, I love it. I went to Singapore for an internship, and you see the Southeast Asian street food, that’s what everyone eats until 1, 2, 3, 4, 5 in the morning.”

Diners seem to be in love with Asian street food. Food-oriented shows such as Travel Channel’s “Anthony Bourdain: No Reservations” have stoked viewers’ appetites for Vietnamese pho and Singapore hawker fare. New York chef David Chang has become one of the most influential figures on the food scene with his Momofuku restaurants, drawing on Japanese, Korean, and other Asian cuisines.

Many have followed his lead. Some of the country’s hottest restaurants are headed by chefs who take Asian cooking and give it their own spin. This spring, two West Coast establishments opened outposts in New York — Mission Chinese Food, where Korean-born, Oklahoma-raised chef Danny Bowien serves what the restaurant has called “Americanized Oriental food,” and Pok Pok Ny, where Portland, Ore., chef Andy Ricker prepares Thai dishes. At both places, people can wait hours for a table.

“There are certain dining trends in the past five years, like the Momofuku empire, that have really made Asian dining more approachable,” says Tracy Chang, a cofounder of Guchi’s Midnight Ramen. “You’re not just tracking down a dark hidden gem in Chinatown or Koreatown or Japantown.”