Feel your pain so much, got a pretty vine from a neighbor years ago that just would not stop. It climbed the fence, the shed, even tried to get into the house. Took me two full summers of hard work to finally beat it back. Learned that lesson the hard way for sure. Now I look up everything, no matter how nice the person giving it away seems.
Yeah the "find out what it is" part is key... I got a plant once that ended up attracting every squirrel in the neighborhood. They dug up everything else trying to bury the nuts near it.