Its chief executive claims it has more users than Twitter. It’s rumored to have just rebuffed a $1 billion buyout offer from Google.

So what’s up with WhatsApp? And how has a San Francisco start-up that many Americans still have never heard of come to lead a fast-growing field of mobile messaging services that are shaking up the phone and Internet industries?

Easy, says Andreas Sanchez, a junior at San Francisco State University who has used a number of such services. “I can text, I can send pictures, I can call, all through Wi-Fi,” he said. “They make it fun for people my age — and, I guess, any age.”

The popularity of online messaging, especially among younger Internet users, has sparked a boom in apps — such as WhatsApp, WeChat, TicToc and Tango — that operate on a mix of advertising and subscription models. By sending messages over the Internet, often via Wi-Fi or mobile data networks, these services let users avoid the text-messaging fees charged by carriers like Verizon or AT&T.

And WhatsApp, by many measures, is at the head of the class.

The company was launched in 2009 by two former Yahoo executives who, unlike the founders of other recent sensations like Facebook and Pinterest, wouldn’t be carded at the local bar. Jan Koum, 36, and Brian Acton, 40, remember not only the dot-com boom but how it went bust.

People who know both men say it’s a big part of why they’ve tried to build the 40-worker company with a minimum of hype.

In a rare interview, Koum and Acton said via e-mail that traditional text messaging is a 20-year-old technology. “We are in the middle of the smartphone revolution,” they wrote, “and it is just beginning.”

CEO Koum, at a New York conference in April, said the service has surpassed 200 million daily users who together send more than 20 billion messages a day.

Greg Woock, head of San Jose, Calif.-based competitor Pinger, looks on such numbers with envy: his start-up carries as many texts in a month as WhatsApp claims to in a day.

But, Woock said, Koum has yet to figure out how best to turn that traffic into dollars.

“His business model is, you pay me once a year, 99 cents,” Woock said of Koum, whom he considers a friend. But that’s only true of iPhone users; WhatsApp is free for owners of Android phones, at least in most countries. “I’d argue,” Woock said, “that the vast majority of his users will never pay.”

Macquarie Securities, in a recent survey of WhatsApp users, found deep passion for the product. While popular features include group texting and the ability to send photos and videos, the greatest appeal is in avoiding texting and roaming charges, especially outside the United States.

Woock — who said Pinger’s user traffic actually outstrips WhatsApp’s domestically — noted that overseas is where the messaging battle is being fought most fiercely. “It’s so expensive everywhere else in the world,” he said.