They are not on any "invasives" list as far as Public Agencies are concerned, but they have invasive characteristics, so you've got to watch where you plant them. They can take over a yard and spread. - quote by Bob, my wildlife biologist/botanist guy.
That said, Bob has planted quite a few rhizomes in our yard! They are fine, if kept under control. I've noticed that some of the cascade crowns/roots/rhizomes whatever they are are under our deck. The hallertauer are spreading near the garden. They really do grow like weeds, and in our area we see old farms with falling barns covered with hops! They aren't growing through the fields, though, or invaded into the woods.