James Martin/CNET

To understand where teens like to spend their virtual time nowadays, just watch them on their smartphones. Their world revolves around Instagram, the application adults mistook for an elevated photography service, and other apps decidedly less old-fashioned than Mark Zuckerberg's social network.

And therein lies one of Facebook's biggest challenges: With more than 1 billion users worldwide and an unstated mission to make more money, Facebook has become a social network that's often too complicated, too risky, and, above all, too overrun by parents to give teens the type of digital freedom or release they crave.

For tweens and teens, Instagram -- and, more recently, SnapChat, an app for sending photos and videos that appear and then disappear -- is the opposite of Facebook: simple, seemingly secret, and fun. Around schools, kids treat these apps like pot, enjoyed in low-lit corners, and all for the undeniable pleasure and temporary fulfillment of feeling cool. Facebook, meanwhile, with its Harvard dorm room roots, now finds itself scrambling to keep up with the tastes of the youngest trendsetters -- even as it has its hooks in millions of them since it now owns Instagram.

Asked about the issue, a Facebook representative would say only, "We are gratified that more than 1 billion people, including many young people, are using Facebook, to connect and share."

There's no hard-and-fast data that quantifies Facebook's teen problem. But we know -- from observing teens, talking to parents and analysts, and from a few company statements -- that age doesn't become Facebook with this group.

In recent weeks, Facebook has told us on two occasions about its teen-appeal problem. When it filed its annual report, it warned investors for the first time that younger users are turning to other services, particularly Instagram, as a substitute for Facebook.

Then, earlier this week, Chief Financial Officer David Ebersman admitted that Instagram, an application he described as popular among the "younger generation," is a "formidable competitor" to Facebook. Which seems odd until you realize that the profit-hungry Facebook isn't yet making a dime from Instagram.

What we do know is that Instagram is already a very popular service that continues to grow rapidly, and we believe, based on the information that we have, that it's quite popular among these kinds of users that you're asking about, the younger generation. It is very important for Facebook to build products that are useful to those users, and to build products that they feel comfortable...they can have a good experience with. Definitely high on the list of priorities for us.

The under-13, tween crowd, including one CNET editor's daughter, technically isn't allowed to use the application, as dictated by the terms of service and a federal restriction (though the law is changing this July in ways that will make it easier for kids to join, something Facebook lobbied hard for). Yet kids found Instagram anyway, largely because their parents wouldn't let them join Facebook, argues Altimeter Group principal analyst Brian Solis. Teens 13 and up joined Instagram, he said, because Facebook became "too great" a social network, where they're now connected to their grandparents.

Isn't it ironic, as Alanis Morissete would say, that Facebook, the onetime underground drug of choice for college kids, is now so readily available and acceptable that we all use it in broad daylight, and worse, at work? Sure, a 12-year-old skateboarder can derive some value from Facebook, but in the whitewashed kind of way that the rest of us use LinkedIn.

"We take pictures of food and landscapes," Solis said, "but teenagers use [Instagram] to share pictures of themselves...the more you share, the greater the reaction, and the more you push outside comfort zones, the more people react."

Screenshot by Michelle Meyers/CNET

Tweens and teens are addicted to the idea of eliciting more reactions in the form of likes, followers, and comments, he said. They employ like-for-like photo tactics, use a myriad of hashtags to get their pictures in front of more users, and promote their desire for additional followers in their profiles.

Ascertaining the extent of Instagram's popularity with teens is particularly tricky -- until you talk to them. And some data on the phenomena does exist. Nielsen, one of the few companies to measure teens' online behavior, can track only Web usage for this youngest demographic. The analytics firm told CNET that Instagram was the top photography Web site among U.S. teens ages 12 to 17, with 1.3 million teens visiting the site during December 2012. By the analytics firm's count, roughly one in 10 online teens in the U.S. visited Instagram in a browser during the month.

Anecdotally, the evidence overwhelmingly points to Instagram as the preferred social network of tweens and teens. A personal relationship provided me with a direct lens to view how two teenage boys used the application in their everyday lives. I also chatted with other kids, some the children of friends, and others I found through friends of friends.

Beth Blecherman's 14-year-old son, who lives in the San Francisco Bay Area, downloaded Instagram when he was 13 because all his friends were using it as their social network. Marisa, a 16-year-old girl who attends Cathedral City High School in Southern California, has been using Instagram for more than a year. She said that a majority of her high school friends are using the application. And a San Diego friend's 12-year-old son is so hooked on the application that he was in tears when his account was temporarily suspended earlier this year. "Teens recognized Instagram as a social network before anyone else," Solis said. "Everyone else treated it as a camera app."

At the same time, Instagram could disappear from teen consciousness just as easily at it arrived. Remember: Instagram was only 17 months old when Zuckerberg bought it in the weeks prior to Facebook's IPO last May. Parents are starting to understand that their kids haven't developed a fascination with the application to share artistic photos of landscapes and architecture. All of the teens I spoke with have watchful parents who keep an observant eye on their Instagram accounts.

Teens searching for a cyberhangout to call their own Adam McLane, a former youth pastor who hosts educational social-media seminars for parents of teens in San Diego, told me that his sessions are dominated by talk of Instagram, with frenzied parents fearful that their innocent young ones are participating in unsavory activities such as bullying or posting inappropriate photos.

Snapchat

The parent factor alone could send kids fleeing to other applications such as Snapchat, Pheed, and Tumblr, all of which appear to have strong teen followings. Investors are betting on Snapchat in particular, which sends more than 60 million short-lived messages daily, because they don't want to miss out on the next Facebook.

"Teens are looking for a place they can call their own," said Danah Boyd, a senior researcher who studies, for Microsoft, how young people use social media. "Rather than all flocking en masse to a different site, they're fragmenting across apps and engaging with their friends using a wide array of different tools.... A new one pops up each week. What's exciting to me is that I'm seeing teenagers experiment."

This experimental nature puts Facebook in the tricky position of reacting to the whims of transitory teens. Take Facebook's impromptu release of Poke, a mobile phone application, modeled after Snapchat, for sending messages that self-destruct moments later. The company's most reactionary move, however, was its surprise purchase of Instagram, an impulse buy that ultimately cost about $715 million.

Now that Instagram has more than 100 million active users, Facebook's impulsive pickup looks like a smart one. But the dangerous reality is that Facebook is bleeding attention to an application with no advertising model, and the social network doesn't even understand how Instagram ties in with its own applications.

Facebook doesn't know what teens want. Ebersman said as much, albeit in less direct terms:

"Facebook is a very young company in terms of the age of our employees, and I am hopeful that continues to be an asset for us in terms of having our finger on the pulse of what matters to that particular constituency of users and how we can provide products to satisfy them."

Put that way, Facebook's saving grace might be that its employees are also tiring of Facebook.