1:30 p.m. EDT We're getting several reports in that elementals and cultists are attacking Azeroth.
1:37 p.m. EDT It looks like there are rifts that open in various zones in Azeroth, and elementals spawn. You can kill the elementals as they spawn.
1:40 p.m. EDT There are quest people you can talk to in Orgrimmar and Stormwind, outside of the banks.
1:49 p.m. EDT You can access a Mysterious Device after you kill a spawn of elementals in any zone.
1:59 p.m. EDT There's an uptick in the number of earth quakes.
2:07 p.m. EDT We're getting reports that this event is now active in the EU as well and the US/NA servers.
2:29 p.m. EDT Tons of quest info in screenshot form after the break.
2:55 p.m. EDT All of the Alliance quests are documented after the break; the Horde quests are very similar.
5:50 p.m. EDT At some point, perhaps not in this phase of the invasion, the elementals will begin spawning in the cities. If you kill them in the city from their big spawn point, then you get a daily quest object/item that lets you go through a portal and kill one of the two new daily bosses for this event: Prince Sarsarun or Kai'ju Gahz'rilla.
That's all we have right now; however, please be aware that we'll update this post with any additional clarifying information we get in.
Lots more screenshots after the break, including many of the quests.