Iguanas are attracted to dense trees and fruit which pretty much describes what Florida is known for. They destroy landscape vegetation, their burrowing speeds erosion, leading to the collapse of sidewalks, foundations and canal banks. They can also transmit salmonella to humans that come into contact with water tainted by their feces.
The Florida Fish and Wildlife says it's open hunting season for all green iguanas, any size, no bag limit, but they must be killed humanly. Personally I will not be killing any iguanas for the simple reason I am unable to kill anything much larger than a mosquito and I find them interesting to look at on the rare occasion I see one.
Update 07/26/2019: Florida Fish and Wildlife has stepped back on the kill directive and now suggests calling a professional to remove any iguanas on your property.