Invasives are plants that do not naturally occur in this region, have a disproportionate negative impact on the environment and can cost homeowners more than they bargained. Some are more difficult than others to remove than others.
A common offender is English Ivy. It is all over the place in towns like South Orange and Maplewood. I have it in my yard and have slowly been removing it for two years.
English Ivy can overtake and weaken trees. If it establishes itself on your house or retaining wall, the ivy can eventually damage it to the point of collapse. Until many native vine plants, English Ivy will work its way into the mortar of bricks causes cracking.
English Ivy is fairly easy to remove. You only have to cut it back to its source. Cutting is the best way to get rid of it. Its leaves are so waxy that chemicals often do not work. Of course, I’m a big believer that chemicals need to be the absolute last step. However you remove the vine, don't put it in your compost pile…you're only a sing for trouble if you do (you do have a compost bin, right?). There’s a some great resources online for getting rid of the vine. Once you have removed all of it, you’ll need to keep an eye out for new clusters pooping up.
If you are looking for a vine for a trellis or fence, Fox Grape or Dutchman's Pipe are great alternatives and are native. Plus with these two options, you will be inviting butterflies and birds to your yard.