killing and removing from trees and around the base of trees. Removing from sides of buildings. Then either cover will chips / Mulch to suffocate out the ivy or roll out black plastic to burn it out. I'd stay away from roundup personally.
Please avoid the use of herbicides, as @Jeremy Smith pointed out. Most of the poison will get into the water table and impact fish, amphibians, birds and mammals, as well as decimating the local flora that we all depend on. Please. Jeremy's advice was excellent and the exact thing we did when we had to handle difficult (because it's invasive) Ivy growing on our plants and strangling them (it came under the neighbors' fence and went to work destroying my herb garden and I fought it off for months). In the winter, I uncovered the root that had made its way under the fence and yanked it hard enough to pull some off the trellis next door (they didn't notice, thankfully). With the help of my husband, I poured wax on it, then lint before the wax had dried and set it on fire. I would not recommend doing that unless you've used fire as a method of plant control in a similar manner before.
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