Well, that's not strictly true. In fact, I'm not even sure if you call what they do living.
A while back, a new drug called 'Longevity' was created, which had the power to extend one's life, theoretically allowing anyone to live forever. But pretty soon, a problem was revealed. People kept having children, and everyone kept on living forever. The world was becoming overpopulated. So The Declaration was created, allowing each family to have only one child and no more. But pretty soon, they decided that was too much too, and so no one can have any children at all.
Of course, some people still dare to defy the law, and those people are hunted down and arrested while any children (called 'Surpluses') are sent to special facilities where they are trained to hate their parents, think of themselves as trash, and to serve Legals.
Surplus Anna is what they call Useful. She Knows Her Place, and is bound to end up a Valuable Asset. That is, until Peter shows up at Grange Hall. Peter is full of strange thoughts and ideas, and insists on calling Anna 'Anna Covey' (even though everyone knows Surpluses only have one name, not two). Peter turns Anna's carefully organized world upside down, and soon she's confused and lost.
I'm really not sure what else to say about this book. From there it goes on as you might expect: Peter finally convinces Anna that her world is screwed up (though it takes incredibly long to convince the poor dense girl), and they run off into the night, etc. etc. There's a dramatic plot twist about Peter's ancestry, and there's various betrayals all throughout the book. So this story isn't exactly overflowing with originality.
Despite that, it actually isn't a bad novel. It's surprisingly disturbing at times, like all dystopian novels should be, but it just didn't pull me all the way in. Peter and Anna were cute, but Anna isn't all that bright and Peter's a tad on the reckless/aggravating side. When I really think about it, there isn't actually anything redeemable about this book except for the thought, "it wasn't bad."
Bottom line: it was good, but not anywhere near great. It doesn't leave a lasting impression, and I'm not going to bother reading the rest of the books in the trilogy. If you want a really good, really disturbing, really thoughtful futuristic/dystopian novel, check out Neal Shusterman's Unwind.