Invasive species can cause serious harm to ecosystems, often out-competing native species.
The economic and biological damage can be significant.
Invasive species can be considered biological pollution and as such we can use externality theory to frame and study the issue. When we get to the topic of solutions, we can also consider addressing invasive species with standards and incentives.
Here's a short article from ENN regarding lion fish and a cool solution ... eat them! I've never eaten lion fish myself (I had one in an aquarium when I was in college), but a student that I had in the Caribbean tells me they're delicious.
Other examples? Other notable solutions?