In areas where they are introduced, they also become quite invasive by practicing something called alelopathy, whereby they introduce toxins into the soil to prevent competing tree species from taking hold.
While I'm at it, Eucalyptus trees have very very dense wood which means the wood burns very hot. This makes it even worse for forest fires where Eucalyptus trees dominate.
(I knew my botany studies would come in handy someday. I just never knew when!)