Purple Loosestrife is an attractive plant I'm sure you've seen along waterways and roadside ditches. Introduced from Europe in the early 1800s, it can now be found over much of the US and Canada. When Purple Loosestrife gets established, fish, bird and wildlife habitat becomes choked out, eliminating native food and cover.
Control methods are uprooting by hand, mowing, cutting, burning and herbicides. Also, four host specific insects have been approved by the federal government for introduction into the US in attempt to control the weed.
A page on the website of Minnesota Sea Grant is a good source for more information. You can visit it here.