The other issue in a lot of southern states (like mine) is privet. People plant it as a pretty evergreen bush that takes heavy trimming in their yard landscaping; but birds eat the berries and spread them far and wide. We loose a lot of nice forest to privet which chokes out the understory and groundcover. It is branching and herty, and once established, very hard to remove. A lot of invasives have a hard time on rocky soil and limestone outcroppings, but not privet. One of the last wonderful limestone cedar glades (very specific habitat with an array of rare & some endangered plants) the nature conservancy seems to have abandoned care for enough that it is almost all privet and very little cedar left. The privet is encroaching into the rest of the open glade as well. All it takes is a seed in a crack of the limestone.
Princess Trees and Persian Silk Trees are another pretty yard runaway which is less prolific than privet but still horrible; and it is choking out native understory trees.