Here in the SF Bay Area, eucalyptus trees are probably the biggest problem regarding non-native plants.  They are all over, unfortunately including many parks.  Their leaves poison the ground so that no plants other than eucalyptus can grow, thereby choking out all of the native plants.  The only way to get rid of eucalyptus trees is to pull them out by their roots, which is generally not practicable or even possible due to the immense amount of work doing so would entail because of their massive numbers.

Many people here who are not aware of the severity of the harms caused by non-natives oppose getting rid of eucalyptus trees because they like trees.  While love of trees and other life is a very good thing, due to their misinformation those opposing removal of eucalyptus take that love too far and do great harm to the native plants and the animals that depend on them.