These so-called thugs are plants that cover the ground so fast that if left to their own devices they eventually crowd out every other plant in a bed.
This plant looks a bit like a stick figure with arms and a small mop of lavender blooms on top, mimicking hair.
Eupatorium coelestinum is a perennial plant with fluffy blue flower heads.
If you want to see a well-behaved garden, visit one that is about three years old.
In my Midwest garden, I have V.chaixii, which is a 3-foot tall perennial with a basal rosette of felted leaves and a tall stalk with tiny yellow flowers.
They are so good at self sowing that once you have one in your garden you will always have them in subsequent years.