The influence of Latin American food on the U.S. cultural palate continues to expand, from not only Mexico, but also from across Central and South America and the Caribbean. From empanadas to chimichurri, there’s an array of Latin food styles and flavors for limited-service operators to consider.

Of course, Mexican fare is a huge influence, joining Italian and Chinese as the big three ethnic culinary styles impacting America. There are 26,000 U.S. quick-service and fast-casual restaurants with a Latin American theme, and all but 1.6 percent of them are Mexican, according to statistics from CHD Expert, a foodservice industry data and marketing firm.

“The Mexican demographic is the largest Latino population in the United States, so it has a bigger influence,” says Brandon Gerson, marketing manager for the Chicago-based company.

Mexican influence is key to many large limited-service restaurant operators in America, including Chipotle Mexican Grill in fast casual and Taco Bell in quick service. And these days, burritos, tacos, and salsas have expanded so far beyond Mexican restaurants that some may not view them as ethnic anymore. Tortilla-influenced wraps have become significant menu items at all types of limited-service restaurants.

Other dishes from Latin America are starting to gain traction, especially in larger cities and Southern border states, as well as Florida. “As globalization continues and cultures mix, you will get different types of cuisines types becoming more popular,” Gerson says.

Many cultures influenced Latin American food, from indigenous peoples to European explorers, particularly Spaniards. The Europeans, including Portuguese, Dutch, and British, brought their own foods and those of regions they colonized.

There’s plenty of opportunity in Latin American food. Research by the National Restaurant Association finds that 80 percent of consumers eat at least one type of ethnic cuisine a month.

“The American palate is still evolving, so it wouldn’t surprise me to see some particular item from Latin America suddenly become very popular,” Gerson says, adding that this happened recently with sriracha, a hot Thai chile sauce.

The proximity and size of Mexico itself provide a variety of cultures and cooking styles that offer plenty of inspiration. Chicago chef Rick Bayless has harnessed many of these at his full-service and fast-casual restaurants, including Xoco and Tortas Frontera.

“We are focused on regional Mexican cuisines and driven by local agriculture,” says Andres Padilla, chef de cuisine for Topolobampo, one of Bayless’s full-service restaurants under the Frontera portfolio.

Frontera has 10 fast-casual restaurants—two Xoco units, three Frontera Fresco restaurants, and five Tortas Frontera locations.

“They’re using the same ingredients as Frontera and Topolo-bampo,” Padilla says of the fast casuals, adding that this includes locally sourced, organic ingredients. “We may treat the food differently, but with the same respect. It’s at a different price point, so we’re able to bring access to more people.”

For instance, cochinita pibil, a Yucatan-inspired pulled pork, uses a similar recipe across all the restaurants. The slow-cooked braised pork—at company-owned units, the wood-fired meat roasts in banana leaves to resemble traditional pit cooking—has an achiote marinade and is served with black beans and spicy habanero salsa.

Tortas—Mexican sandwiches on baguettes—are key at Frontera’s fast-casual units, although Frontera Fresco also has burritos and tacos. The tortas include cochinita pibil, as well as pepito (braised short ribs with caramelized onions and other ingredients) and ahogada (pork carnitas with black beans, tomato-arbol chile broth, and pickled onions).

A Zagat consumer survey earlier this year ranked Tortas Frontera the top fast-casual restaurant in Chicago. Another Mexican fast-casual chain, Torchy’s Tacos, was tops in Dallas and Houston.

“We call it gourmet street food,” says Michael Rypka, vice president of culinary and marketing, who began Torchy’s in 2006 out of a trailer. Most menu items are made from scratch at the chain’s 31 restaurants in Texas (another unit is set to open in Denver).

“I’d say there is a decent amount of influence from interior Mexican food, but then we add our own layers on it,” he says.

The Mr. Orange taco, for instance, is reminiscent of something one might find in Veracruz but with a twist: It has blackened salmon topped with black bean and corn relish, queso fresco, cilantro, and an avocado salsa drizzle on a corn tortilla.

Other tacos feature grilled, fried, and stewed meats and fish—even Jamaican jerk chicken. Various other ingredients, including vegetables and chile-infused salsas, play a role in the tacos. Torchy’s also features a taco of the month, like September’s Tipsy Chicken with homemade maple bacon and bourbon marmalade. “It’s a really good way to test items,” Rypka says, noting that about 80 percent of the menu began as a monthly offering.

Burritos originated in northern Mexico, but the recently evolved assembly-line preparation style—popularized by Chipotle—is rooted in the taco vendors in San Francisco’s Mission District that started dishing them a half century ago. These burritos are made with large flour tortillas filled with a protein, beans, rice, salsas, and other ingredients.

New York’s Dos Toros, which launched in 2009 to capture the San Francisco taqueria style the founders grew up with, has grown to nine stores in the Big Apple.

“We are built to be self-contained, so [each unit] does everything in-house,” says Leo Kremer, who owns the business with his brother, Oliver. “Grilling jalapeños, cooking from dried beans, making carnitas every day, even something as simple as rice, speaks volume.”

Burritos are heated in steamers to melt the cheese. Dos Toros’ tacos are larger than traditional taqueria style, and its quesadillas are like folded, crispy burritos, not tortilla disks with melted cheese.

Carnitas are the measuring stick for Mexican-style restaurants and a signature item at Dos Toros, he says, even though more grilled chicken is sold. “We sear and then slow cook it for hours,” he says. “It’s the most difficult protein, and no one here does it like us.”

Any spiciness and heat in Dos Toros’ food is from the sauces, which include classic chile verde, smoky chipotle, and a hot habanero sauce that carries a floral-citrus flavor, Kremer says. The sauce is usually applied on the preparation line.

Empanadas—pastries stuffed with meats, vegetables, fruit, and other ingredients—are an item popular to cultures across Latin America. At Mr. Empanada, which has nine restaurants in the Tampa, Florida, area, the empanadas are Cuban-style and fried.

“This is what we kind of grew up on,” says Audrey Perez, chief executive of the family-owned business. Traditional Cuban empanadas include ground beef, crab, or guava with cream cheese, but Mr. Empanadas features a dozen varieties. All of the company’s empanadas are made at a central location, frozen, and sent to stores.

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“We position ourselves as a gourmet empanada, with fresh vegetables, no fillers, and the best tomato purée in sauces,” Perez says.

While family recipes helped create Mr. Empanada’s fare, the company didn’t want flavors that were too strong or hot to appeal to a mass audience, she adds. The chain also offers Cuban sandwiches, a pressed ham-and-cheese Florida favorite now popular at all types of American restaurants.

Empanadas are also on the menu at Peruvian Brothers’ two food trucks in Washington, D.C. This version is baked, filled with beef, chicken, or spinach and cheese, and topped with powdered sugar and a slice of lime.

“We’re combining saltiness, sweetness, and savory in one bite,” says Peru-born Giuseppe Lanzone, who launched the business with his younger brother, Mario. “You can’t have a Peruvian menu without empanadas.”

Many other dishes using family recipes fill the menu, including sandwiches like Pan con Chicharron, which has salted pork tenderloin and criolla sauce, and Pan con Asado—roast beef with caramelized onions.

“We’re from the coast, so you go to the beach, and part of that is going out and having a sandwich,” says Lanzone, who was a former member of the U.S. Olympic rowing team after immigrating. “The chicharron was the first thing on the menu.”

Criolla, with onions, olive oil, vinegar, lime juice, and seasonings, is “put on everything you have in Peru,” he adds. The brothers also have a salad with quinoa, the Andean grain that’s gained popularity at restaurants across the U.S.

To the east of Peru is the huge nation of Brazil, home of limited-service chain Giraffas. The company has nine fast-casual restaurants in Florida.

“Everything we do here is cooked to order,” says Rene Prats, president and chief executive of the U.S. business. “The quinoa is organic; the beef is USDA Black Angus; we use all-natural chicken; and the sauces are all fresh.”

The most popular meat in Brazil is picanha, a beef top sirloin cut that Giraffas ages for three weeks, he says. The meat is often served with chimichurri, a popular green sauce originally from Argentina that includes herbs, garlic, olive oil, and vinegar.

Grilled picanha is served alongside white or brown rice, black beans with garlic and bacon, and a third side, such as a quinoa salad or farofa, a national dish Giraffas prepares with toasted manioc flour, scrambled eggs, bacon, olives, and parsley.

Frejoada, a stew of beans and meat with Portuguese roots, is served only Wednesdays and Saturdays. Every two months, Giraffas brings a different Brazilian dish to the menu, and the U.S. restaurants recently added pork picanha that “eats like steak,” Prats says.

Like empanadas, pinchos—Spanish for skewer or kabobs—are popular across Latin America. At Pincho Factory in South Florida, the namesake items are beef, chicken, or shrimp kabobs served on wraps or bread or in salads or rice bowls.

“We put a lot of love in our food,” says Nedal Ahmad, cofounder and chief executive. “The processes are easy, but good food takes time.”

There are seven pincho styles, like Fresco with diced lettuce, tomatoes, cucumbers, and cilantro sauce, or Chipotle, which has pico de gallo, jalapeños, and chipotle mayonnaise.

Pincho Factory also serves burgers, including some using various Latin American flavors, since South Florida “is the melting pot of cultures,” Ahmad says. The Toston has two deep-fried plantains instead of a bun, and the Nicaragua-influenced Fritanga burger is topped with fried white cheese, cabbage slaw, and crema.

Monthly specials include dishes like Croquestesa—chuck, brisket, and short rib made into a Cuban-style croquette and topped with Swiss cheese, mustard, pickles, and mayonnaise on a brioche roll.

When it comes to Caribbean cuisine, there are many choices, and Pollo Tropical draws from numerous nations in the region, particularly the Greater Antilles. Most of the influence is Spanish, but there are others; Jamaica, for example, is a British commonwealth, so it’s not unusual to find hot spices from former British colonies like India.

“The further you get from South Florida, Caribbean food tends to be known more as Jamaican,” says Jeff Webb, vice president of research and development for Pollo Tropical, adding that Jamaican cuisine is known for jerk and other strong spices.

The chain is chicken-centric but also has dishes like Cuban-influenced Mojo Roast Pork, which is slow-roasted in a mojo juice blend. There are also tropical favorites, such as fried yuca, yellow rice, and caramelized plantains.

Pollo Tropical’s jerk spices and curry mustard sauce—curry, mustard, and mayonnaise—are examples of how some Caribbean flavors are toned down for an American audience.

“There is a huge fear of jerk among some people,” Webb says, noting the real deal often needs to be sweetened for American palates that are still evolving. “It’s the same with Indian curries. They’re extremely polarizing, and you have to lighten them up.”