Hasn't been mentioned here yet, but, to get rid of the stuff there are two things I use. Roundup (or equivalent) works but I use the concentrate so I can beef it up. But Roundup is a nuclear option and kills everything. I've also had success with 1 part household/laundry bleach 2 parts water. It kills the ivy but leaves everything else. The bleach reacts with the oil and the leaves loose their protection and die. Got this from my BIL who is a chemist and looked up the formula for the base in the oil and said give it a try. Bleach does not kill down into the buried vine like Roundup, so you'll be doing the application for a few seasons until you starve out the root. But you don't always have the luxury of laying the landscape to waste just to get rid of some ivy.
Pete