Then there are native invasives, like Dog Fennel in pastureland. Florida does not like to be turned into pasture, it likes to turn into scrub forests and swamps, and Dog Fennel is a succession plant that helps with that process. It quickly flowers and reseeds itself over an entire field, ruining it in just one season. (Maybe that's why Florida has no large land herbivores?)The agricultural state university 'round here is doing trial testing for releasing a beetle that eats Air Potato. While I'm all for getting rid of Air Potato, a member of the yam family from Africa that may or may not be edible, I'm unsure that the beetle is the way to go. UofF was also responsible for the Lovebugs being introduced here, and look how well that turned out! The Lovebug's only natural predator is... cars driven by humans.
The extension service agents and the university website will both point out chemical controls for various plants, and how to properly apply them. This technique could be useful for a very small infestation of a particularly noxious plant, like Poison Ivy, but how would it work for an acre of forest covered by Air Potato or a field infested with Dog Fennel? On the other hand, proper land management techniques are generally cheap or free, excepting for time investment.
Some techniques: controlled burns, agro-forestry, tilling and seeding, over-seeding, frequent rotational grazing, overgrazing and seeding, hand-scything, rotational grazing with multiple species, holistic management. Perhaps really rethinking how agriculture is done here might include something even more drastic, like small-scale, holistic, organic farms that raise key deer and rabbits instead of cattle.