The buckthorn stops here

On Memorial Day, my dad came over to give us some sage advice.
My dad can identify just about any plant, bug or animal. If it grows, he can ID it.
We bought our house in October, too late to do much about the greenery, so he came Monday.
I hoped for good news.
I was wrong.
Turns out a good chunk for our landscaping is buckthorn, an invasive plant that kills all the stuff you actually want to grow. What used to be a long line of lilacs had one surviving bush. There are a ton of mulberry trees but none of them seem to be growing in places that are conducive to trees. (If I have to choose between the garage and a mulberry tree, the garage wins, even if that's not an eco-friendly choice.)
We have a MASSIVE pine tree behind our house. I'm terrible at heights, but it's probably the equivalent of a three-story building.
"See that," my dad said pointing to the top of the tree.
"What?" I said, squinting.
"That green stuff," he said. I stared at him. It was all green. It's a pine tree, for goodness sake. I wisely shut up and looked.
Yep, he was right. Something the wrong green was poking out near the top.
"Grape vine. Kill it before it kills the tree. Just cut it off at the base," my dad said.
Grape vine? What's grape vine doing there? Growing happily is what. At the base of the pine tree, the grape's vine is wrist-sized. But now it's got to die or else the tree will suffer. In the rock-paper-scissors world of botany, tree beats grape vine when it comes to my love. And everything beats buckthorn.
How bad is buckthorn? In 2004, Illinois made it illegal to buy, sell or plant buckthorn in the state. This is Illinois, known for corruption. If they say it's bad, it's really, really bad.
The buckthorn bush-tree-things are massive. They look like regular shrub-bush-things, but they grow everywhere. They cover all of the good bushes, taking up the sunlight and the water and ... well, everything good.
So we spent a few hours sawing out massive buckthorns, creating a pile that makes it look like the tornado struck again. The job is far from over. We're going to be on buckthorn duty for a long time. With luck, some of the lilacs will return. With luck, the honeysuckle will recover from being beat down. With luck, some grass will grow in the dirt long kept covered by buckthorn.
Are you battling plants in your yard? Do you know what plants can strangle the good ones and leave you with undesirables? I confess I don't have that knowledge. If you don't either, borrow someone's brain and let us know what the situation is like in your yard.