Luke trained a generation of new Jedi, including his nephew, Ben, who eventually turned on him, killing all the other Jedi. After this, Luke went on a quest to find the first Jedi temple and disappeared into exile. But why? This is nothing like the Luke Skywalker we know from the original trilogy - the one who leaves his home to save a princess he doesn't know, abandons his training to save his friends on Cloud City, gets captured by Jabba to save Han, and eventually turns himself over to the mercy of the Emperor because he believes there's a shred of goodness in his father still. So what could happen to crush the hope and devotion seen in the younger Luke in order to turn him into an old man that retreats to an island, abandoning a budding galactic war, and refuses to even rush to the aid of Han Solo, who's peril he could certainly sense if he could detect the danger to his friends on Cloud City when he was still training? Now, he lives in isolation, thinks the Jedi need to end, and apparently clashes with Rey - if the trailers can be believed.
The puzzle pieces of this collapse are all available in the known story. If Kylo Ren killed the rest of the Jedi, he probably also faced off against Luke. Based on the trailers, it looks like Luke was left for dead, meaning his apprentice had gained the upper hand in their confrontation, possibly by damaging and disabling Luke's lightsaber as we've seen done in a number of lightsaber fights before. Having lost all of his Jedi students, knowing he trained the person that killed them would be a major blow and a major source of pain for Luke. This pain could easily give way to anger and hatred, driving him to seek vengeance on his nephew and Snoke.
But first, he'd need to rebuild his damaged lightsaber. The only problem is, having given into his hatred, he would have caused his crystal to bleed during the reconstruction, turning his green saber red, a symbol that would doubtless be a convicting one for the son of Vader. Shocked by what he'd allowed himself to become, fearing that even if he kills Kylo, he would only be perpetuating a dark cycle, he retreats in search of ancient Jedi truths, wearing his now-red kyber crystal around his neck as a reminder of his failure.
The Luke we see in trailers for The Last Jedi may not have entirely succumbed to the dark side, but he's very likely living in fear and shame of his many failures. This fear, of course, makes him wary of Rey's ability as well, but hopefully she'll return hope to the old Jedi and convince him to join the fight once again. Either that, or she gets captured (again), forcing him to go rescue her, raising his X-Wing out of the sea, and reconstructing his lightsaber, in which case, he may actually wind up with a white blade, a first for a Star Wars movie after Ahsoka Tano was the first known character to purify red kyber crystals in her own sabers in the Ahsoka novel.
There are plenty of unknowns about this movie, giving way to a number of shaky theories, but what makes this particular explanation such a convincing idea is that it's is a single answer that ties together a number of mysteries for The Last Jedi: Why did Luke run to exile, why aren't they showing his green lightsaber in promotional material, why is he wearing a red kyber crystal around his neck, and what happened when Ben turned against him? This single answer also utilizes a swath of Star Wars lore that either doesn't require detailed explanation or can be easily explained with a few lines of dialogue in the movie. The audience doesn't need to know why kybers turn red or who Ahsoka Tano is, just the visual image of Luke igniting a red lightsaber and the blades turning white should be enough of a twist on classic Star Wars iconography to thrill the audience.