They have thrice invaded Azeroth and were only beaten back at a terrible cost. Much of Azeroth's history — including the First, Second, and Third War — were due to the Legion's influence. It can be said that the Legion is Azeroth's nemesis; it corrupted the orcs who then invaded Azeroth, created the Lich King, and is the source of most of Azeroth's scars. It should also be noted that Azeroth is the only known planet that they have ever failed to conquer.
The Legion's mission in theory is to undo the works of the titans and restore the universe back to its original, chaotic and disorganized state. In practice, the Legion scours all life from the worlds it invades; they are cursed to roam the greater realms forever, consuming the primal energies of magic to survive.
The Legion has destroyed world after world in its mad lust for arcane power and is thus responsible for the genocide of thousands of races across the universe, totaling in billions, if not trillions of lives.