By definition (specifically Executive Order 13112 signed in 1999 by President Clinton), invasives are organisms that (1) are not native to the area in which they are being found, (2) are capable of escaping cultivation, and (3) can out-compete native organisms causing harm to human health, the economy or the environment. Invasive plants too often become a problem because we humans fall for the attractive qualities of a non-native plant and use it extensively, providing an expanding pool from which it reproduces itself. Spanish Bluebells are now on the invasive list. Check out this article to see what plants make a good replacement for them.