Waves are groups of Greed unleashed from a portal. They can be composed by one silly greedling, by a mildly strong pack of assorted Greed, and even by an absurdly overpowered, seemingly never-ending stream of monsters.
With the exeption of floaters, all waves as a whole target the Monarch—who will hopefully be found behind the protection of a wall. They will destroy and plunder the obstacles in their path, until they get what they want: the Crown.
The Greed will always attack the Kingdom in waves.
Every night, active portals send out a number of greedlings. As the Kingdom progresses, the attacks become more and more powerful, eventually including floaters as well as breeders. Every day at noon, portal activity shuffles to keep the Kingdom on its toes.
Kingdom: Classic – When a portal is destroyed, an immediate swarm of greedlings, floaters, and breeders pours forth from the closing portal. The knights and their archers can often perish, especially if they lack the blessing from the Statue of Archery. These waves get more massive the more portals have been destroyed, and can level an unprepared Kingdom. Being a long way from the outer wall may result in the attack troops being destroyed.
Kingdom: New Lands and Kingdom Two Crowns – When a portal is destroyed, the sky is blacked out as if by solar eclipse, and the next Moon appears red. These are indicators that the Greed are preparing a counterattack. Unlike in Kingdom Classic, the Monarch troops here will always have enough time to run back to safety, no matter how far they are from the walls. With a deep rumbling/grinding sound, a random portal spawns dozens of greedlings and possibly floaters or breeders to attack the Kingdom. The solar eclipse remains until the counterattack is dealt with, at which time the normal day-night-cycle resumes from where it should be. Time still passes, so the sun can be just setting when the shadowy sky lifts. The sound of bells indicates that the Kingdom is safe again. The more portals are destroyed, the stronger the retaliation waves become.
See Blood Moon.