You can screenshot images however this takes great skill on some devices and if you do manage a notification will be sent to the person who sent the picture informing them that you've saved it.
So why are teenagers addicted to it? I'll admit that I hated this app when I first downloaded it. I hated the fact that once pictures has been seen they were gone forever and I just didn't see the point of sending just pictures of myself. So after only a couple of hours with the app I deleted it.
One week later I was forced to reinstall it again by my friends and now I'm addicted. I refresh my snapchat now almost as much as I refresh my Twitter. Most of the time I'm not in the mood to text people or even make small talk over Facebook Chat so I now send my friends a quick snapchat of my smiling face with a small message for them to read.
Obviously though, not every person will use Snapchat for the same short gentle messages like what I send. Snapchat processes 150 million images a day, some of them will be kind and friendly others might not be (if you get me.) Since pictures are gone and never to be seen again after less than 10 seconds some people have taken this opportunity to send pictures that will never be seen again after 10 seconds (if you get what I mean).
I think most teens will just use snapchat as a simple way to have simple conversations. Most teens like taking photos and most teens don't like writing much so this app has successfully combined those two things and snapchat now has millions of users. Snapchat was developed by university students so it is not a surprise they know what teenagers want out of an app. 2 years since launch and snapchat is bigger than it has ever been.
Under 13's can use a similar app made by the same people of snapchat. The app is called Snapkidz and is extremely similar to the original snapchat app. It allows children to take photos, add annotations and then save them onto their device (not send them).
Anyway, it is inevitable that adverts are going to get added to Snapchat in the near future however we are still waiting to learn how they are going to be displayed in the app and where they are going to be.