Organic food is supposedly all the rage. Sales of food made without conventional methods or additives like pesticides and hormones increased 8.4% last year compared to an overall increase of 0.6% in U.S. food sales.

However, in the restaurant industry, the once-vaunted fast-casual chains that were supposed to take over the industry have mostly flopped. Chipotle Mexican Grill, the poster child for "Food with Integrity" has struggled to rebound following its 2015 E. coli crisis, and chains including Noodles & CompanyPotbellyZoe's KitchenEl Pollo Loco, and Habit Restaurants all have lost more than half of their value since their IPOs a few years ago. 

Meanwhile, fast-food stocks have thrived. The narrative that millennials are rejecting traditional fast food simply doesn't seem to be true. Here are five fast-food chains the young-adult generation continues to embrace.

The front of a Wendy's restaurant

Image source: Wendy's.

Wendy's

Arguably no fast-food chain has won over millennials more than Wendy's (WEN 1.97%). The company's Twitter account has become famous for snarky comments and roasts of rival fast-food chains. 

Wendy's was also the source of the most retweeted tweet when the company challenged a fan to get 18 million retweets for a year of free nuggets.

Carter Wilkerson managed to get 3.6 million retweets, and Wendy's awarded him free nuggets anyway.

Millennials count for a quarter of Wendy's customers, and in addition to the social media approach, the company has rolled out kiosks for ordering and menu items like pretzel buns. As a result, shares have soared as same-store sales have moved higher, bucking the broader industry trend.

A McDonald's restaurant

Image source: McDonald's.

McDonald's

The traditional fast-food leader has been a winner among millennials lately. The company's launch of all-day breakfast was warmly embraced by young people, as no demographic had clamored more for an Egg McMuffin after 10:30 AM than them.

McDonald's (MCD 0.10%) has made other moves to target millennials, such as improving its McCafe line, pressuring Starbucks' base, and adding ingredients like sriracha that are popular with the young generation. McDonald's stock is now trading at all-time highs on strong sales growth in the U.S. and abroad. 

A Domino's location

Image source: Domino's Pizza.

Domino's Pizza

The pizza-delivery chain has been the best performer of all fast-food restaurants in recent years, with comparable sales jumping by double digits in most quarters and the stock up more than 300% over the last five years. 

Domino's Pizza (DPZ 1.05%) successfully targeted millennials by giving the famously phone-adverse generation multiple platforms to order through, including tweets, texts, and emojis. The company's pizza tracker also gives customers a fun way to know when their order will arrive.

It doesn't hurt that both pizza and delivery are popular among millennials. The money-transfer service Venmo said pizza is the most common purchase among 20-somethings.

The front of a revamped Arby's restaurant

Image source: Arby's.

Arby's

This one may seem like a surprise, as Arby's was once roundly mocked by former Daily Show host Jon Stewart, but the roast-beef chain has garnered a following among millennials thanks in part to its "We have the meats" ad campaign. Privately held Arby's same-store sales jumped 8.1% in 2015, and it's now posted 28 straight quarters of comparable sales growth. The share of millennials visiting its restaurants surged from 38% to 54% in just two years.

Stunts like buying Pharrell's Arby-like hat for $44,100 on Ebay have also helped the company build brand buzz.

A chicken quesadilla piled up in quarters

Image source: Taco Bell.

Taco Bell

Taco Bell has targeted millennials in a wide range of ways, and it's paid off: same-store sales have increased in 11 of the last 12 quarters. New menu items such as the Doritos Locos Taco have been a hit with the younger crowd, and the company has even begun opening "Cantina" locations that serve alcohol, a unique move among conventional fast-food companies that have traditionally marketed to families.

Through its Live Mas campaign, the Mexican-food chain has embraced bands, awarded scholarships, and even launched a clothing line with Forever 21, another idiosyncratic choice for a fast-food brand. Those moves have helped make the chain Yum! Brands(YUM -0.47%) crown jewel as it's easily outperformed Yum's other two brands, Pizza Hut and KFC.