Though we haven't been able to spot it in any of the teasers, Luke Skywalker will apparently have a necklace in The Last Jedi, and it will be connected to Darth Vader in some way. Whether it's important to the narrative or just a piece of lore, the necklace has opened up another door of speculation.
According to Making Star Wars, Luke is said to have kept pieces of Darth Vader's lightsaber, and their source says that Luke will have a necklace that will have a red crystal protruding from the bottom of it — possibly the Kyber crystal in Vader's weapon.
With that in mind, it's possible that Kylo Ren may want to get his hands on this crystal as well. After all, his crossguard saber is considered to be rather unstable since it was crudely assembled and it has a cracked crystal in the middle of it.
I'm just curious as to how the crystal will factor into the story, since, after the Ahsoka novel, it was revealed that there were no such thing as red Kyber crystals. Since the Sith can't form a bond with crystals like the Jedi can, they are forced to steal the crystals from previous users. They would then force their will on the crystals, causing the blades to "bleed" red.
Hopefully that fact is explored more in The Last Jedi, because if not, then we're looking at another big plot hole in the universe. I think a lot of us will be curious as to who previously owned the crystals and how it got into the hands of the Dark Side users.
Some part of me also wished that the necklace that Luke had would be the japor necklace that Anakin gave Padme in the prequels. That would have been an interesting callback.
Star Wars: The Last Jedi comes out Dec. 15.