Map showing distribution of the mosquito (Aedes albopicta). Centers for Disease Control.
One of the first questions people invariably ask when told of an invasive species is - "Where is it?". Nothing shows that better than a distribution map. Maps are created at many different spatial scales and for many different purposes. One nice attribute of a geo-spatially produced map is that you can relate occurrence points to other attributes of the area such as temperature, soil, vegetation type, etc. That is the first step towards modeling and predicting where invasive species may spread.
The following sites provide distribution maps for various introduced species:
to obtain more information.