In The 5th Wave, the end of the world is occurring in stages otherwise known as "waves." (You can't rush a good alien apocalypse, people.)
The first three occurred before the book began. The First Wave involved an electromagnetic pulse that snuffed out all lights and machines. The Second Wave (no pun intended) was a series of tsunamis that obliterated the coasts. The Third Wave was a nasty virus that made people bleed out of their eyes. We're not gonna lie: that one was pretty gross.
When the book begins, survivors like Cassie are being hunted down in the Fourth Wave. It's being led by a group of highly skilled alien ninja types. For the Fifth (and final?) Wave, the aliens are training child soldiers to wipe out their fellow humans.
We get that intel about three-quarters of the way through the book. See, part of the tension in the story (for us and for characters like Cassie) is wondering what treachery the aliens will try next.