In retrospect, once you realize what DC's New 52 initiative really is, Teen Titans would have always been one of the perfect bridges between old and new continuity.
Back in the '80s, New Teen Titans was one of the top selling comic books in the whole medium. One of its defining stories was "The Judas Contract," one of the rare (for that time) story arcs that rewarded loyal readers when teammate Terra was revealed to be a pawn of Deathstroke the Terminator. It was a era for the team that introduced the likes of Starfire (now featured in Red Hood and the Outlaws) and Cyborg (now featured in Justice League) to the DC landscape.
A lot of Teen Titans comics have tried to duplicate that era over the years. There was a whole Dan Jurgens run that attempted to introduce an entire line-up of new characters. Perhaps that was a little too ambitious (or his '90s youths weren't what actual '90s youths were interested in at a time of Gen 13 and Generation X, among the most popular comics of that decade).
Scott Lobdell's Teen Titans, now in its third volume of collected adventures, has a couple of brand-new characters, the Latino youth known as Bunker and the mysterious Solstice, who in the issues collected here is represented as full of the classic Titans tradition, a mystery just waiting to unfold. Tellingly, perhaps, another from that tradition, Raven, makes appearances late in the collection. If Solstice ends up anywhere near as iconic (Raven was a key presence in the Teen Titans Go! cartoons that reintroduced the team to a new generation), Lobdell might have finally figured out how to make these guys popular again.
What makes the Titans so relevant today to what they were doing thirty years ago? The New 52 landscape is an attempt to hook readers all over again by drawing them in with storylines, continuing arcs that develop over years. That's the '80s Titans in a nutshell, an early adopter of a model that has come to increasingly dominate comics. Another of the signature New 52 titles, Scott Snyder's Batman, is one such series, for instance, and the source for the crossover arc represented in this collection.
"Death of the Family" is the New 52's attempt to make an icon out of the Joker all over again. In this arc, the Clown Prince of Crime kidnaps each of Batman's allies to try and prove that they're detrimental rather than helpful to the cause (although this is as much a self-serving gesture as anything Heath Ledger pulled in The Dark Knight, no matter what the guy says). The gimmick that dominates this new era of the Joker is his new peeled-face-as-a-mask look, but really it's the character much as he always was, just a little more focused than usual. He's obsessed with his legacy, his relationship with Batman.
The Titans have Tim Drake, the third Robin, as their leader. The second Robin, Jason Todd, is leader of a team of Outlaws who were in a previous era signature members of the Titans (including Starfire). Both Tim and Jason are represented here in full, all relevant issues of Teen Titans, of course, as well as one from Red Hood (and the helpful concluding issue from Batman, which to my mind hints at a far bigger story Snyder has in mind).
The collection also includes the Zero Month issue from September 2012, which is Lobdell's version of Tim Drake's origin, which stresses Tim's fairly perfect childhood that somehow still wasn't satisfying or perhaps challenging enough to dissuade him from pursuing Batman as his next sidekick (a story originally told in the excellent "Lonely Place of Dying" arc that followed "Death in the Family" from the late '80s). Tim was the first Robin to have his own ongoing series. This new version of his origin suggests there is plenty left to tell about his formative years. If he ever gets his own series again, that would be a great place to start, and perhaps more accessible to new readers than the sometimes cluttered Teen Titans adventures.
If there's any failing in this collection, it's in a lack of clarity. You probably wouldn't want to start here, for instance. The blessing and the curse of the New 52 initiative is that it makes these collections as mandatory to continue reading as all those manga volumes I'm sure DC was thinking about (imagine if these collections were digest size!). The Solstice story doesn't end here. There's a recent Kid Flash story that explains his updated origins. I don't know if Bunker will become an actually interesting character (he's boasted as a future Justice Leaguer in this collection, although he'd have to develop far more to reach that point; for now his look evokes nothing more than an Alpha Flight reject, while his powers make him out to be a more limited version of a Green Lantern), but he's the weakest showing here, at least in costume. These characters, along with every other teen character in comics, could always benefit to step out of their superhero guises more often.
If you believe in the potential of the series, though, this is a great place to look, and a fine example of how it fits in with the rest of the New 52 landscape, as potentially one of its future headlining acts.