Okay, I think I'm starting to get it! Man is this convoluted! I'm going to put down what I think I understand, because I may need to refer to it when I read later volumes.
1. The Baskervilles are in charge of watching over the Abyss.
2. Glenn Baskerville is not actually a name, but a job, the head of the Baskervilles. It is passed on by each Glenn via transferring the contracts between him and five "black-winged chains" to a new Glenn. (These chains are Raven, Jabberwocky, Dodo, Owl, and Gryphon.) When Jack Vessalius enters the picture, the current Glenn is Levi, but he is about to pass the position on to Oswald.
3. People who are weird, and around whom weird stuff happens (they "create anomalies") are often summoned to become Baskervilles. A common anomaly created by those who are destined to become Glenn is a sibling who is a "child of ill omen," a person with red eyes. Children of ill omen are considered dangerous by the Baskervilles, because they are the only people besides Glenn who can open the door to the Abyss. Therefore, when a new Glenn is instated, he must kill any child of ill omen who he "created" (i.e. with whom he was close, typically a sibling).
4. Jack Vessalius is homeless and starving, the bastard son of a nobleman, when he meets Lacie, a capricious child of ill omen who ran away from the Baskervilles because her brother, Oswald, was mean to her. They have some adventures, and she makes him care about his own survival, and then she goes back to the Baskervilles. Jack spends the next eight years doing anything necessary to take his place as a noble and see Lacie again - including, it seems, making deals with a psycho named Miranda who wants the head of Lacie's brother Oswald. Jack does take his place as a noble, and he gains an open invitation to see Lacie, which he frequently does.
5. Oswald becomes Glenn, and he casts Lacie into the dark heart of the Abyss, which is a death sentence. First, though, Levi asks her to participate in an experiment. The experiment? Levi will impregnate Lacie, and then they'll wait and see if the Abyss spits out any babies. For some reason, Lacie apparently agrees to this.
6. The Abyss spits out a baby. They name her Alice. Apparently Lacie had twins, though? There's a White Alice and a regular Alice, and I think maybe the White Alice is the Intention of the Abyss . . . it's confusing.
7. Jack Vessalius discovers Gilbert and his younger brother Vincent, who is a child of ill omen. He tells the Baskervilles about them, and the Baskervilles take them in. Gilbert starts being groomed to become the next Glenn.
8. Lacie created two toy rabbit while she was in the Abyss. She kept one and gave one to the Intention of the Abyss . . . I think? Anyway, Alice has one now, and she names it Oz, presumably after Oswald. But Lacie sends that toy rabbit to Jack, and when he touches it, he learns of Lacie's feelings for him - and that he can't bring her back from the Abyss, which is what he'd been trying to figure out how to do. So instead, he decides to fling the world into the Abyss and join Lacie that way.
9. Jack asks Alice to help him make a chain that will be able to accomplish this. She says he should make it out of the toy rabbit still in the Abyss, and she names that one, too, Oz. They need someone to open the door to the Abyss, though, so Alice tricks Vincent into doing it. (Remember how a child of ill omen can do that?)
10. Oswald, seeing that the world is coming unmoored, manages to limit the effects to just the city of Sablier. He then goes about killing all the people in Sablier, because if they fall into the Abyss, it will mess with their souls in some way. They'll become chains, or something. Not good. Anyway, hence the tragedy of Sablier. And this is basically what everyone knows, that Glen (Oswald) Baskerville snapped and started killing everyone in Sablier, and then the city sank into the Abyss. Jack Vessalius left out the other stuff.
And NOW, Leo has taken up the Glenn mantle and used his power over Gilbert to make him shoot Oz, who it turns out was a chain all this time! (Kind of makes me want to reread earlier volumes to see where that might be set up.) Gasp!
Also, we see Xerxes Break a little, but not nearly enough. MORE BREAK! I DEMAND IT! But on the plus side, Vincent is seeming less evil at the moment, which makes my Xerxes/Vincent notions look better all the time. If still not very likely.