Babylon Towers was a building of elite luxury apartments for the extremely wealthy in Gotham City.
It was designed as a self-sustaining system with an indoor mall, so residents would never have to set foot outdoors again. They sealed themselves off during the Contagion event, when Daniel Maris warned them the Apocalypse Virus was coming to Gotham. Maris was secretly an Order of St. Dumas agent who had been infected, and he unknowingly spread it to the entire building. This effectively put them into quarantine, although it was too late as they had already dismissed their servants. When Maris began showing symptoms, they realized their mistake and bargained with the Penguin to help them find a cure.
Batman believed he had developed a cure, and sent Poison Ivy in to test it on the infected. The inside of the building had become a nightmare, piled with corpses while the rich indulged their last moments in orgies. Instead of helping them, Ivy blackmailed the residents before revealing that her cure didn't work anyway. Outside, angry rioters set fire to the building. Batman and Jim Gordon were barely able to drag Ivy out of the burning building before it collapsed and killed everyone inside.