Invasive. When a gardener tells you a plant is invasive, and asks you if you still want it, you should think carefully before you jump up and down and say yes, please, I've got lots of room. I'll take ten.
Trust me on this. Those tall flowers in the photo above? Aster tartaria. Beautiful purple blossoms with yellow centers, six or seven feet off the ground. The plants bloom in late September, making them a boon to perennial borders filled with plants that peak earlier in the season.
I started with ten aster tartaria plants. Now I have hundreds.