Hesperis matronalis-Dame's Rocket. Considered invasive....for me it's second or third tier invasive, in other words, not a top priority. I say this simply because wherever I've ever seen it growing, what would otherwise be growing in that location would be burdock, reed canary grass, Canada thistle, or some other less-than-desirable species. Plus, it has pretty flowers. I'm weird that way. Some practitioners go after this one with gusto.

Yep, not a native wildflower, it is native to Eurasia. But it has naturalized pretty much everywhere in the temperate world :-) As tom mentioned it is seldom considered a 'true' invasive as it does not really crowd out native plant growth but it does self seed with abandon and many consider it more of a weed than a valuable garden plant. But it IS sold for that purpose :-) Lunaria annua (money plant, honesty) and Centranthus ruber (Jupiter's beard or red valeran) are very similar in this regard - often planted intentionally but just as frequently seen popping up along roadsides or in untended spaces.

Here in Michigan, Dame's Rocket is highly invasive, along with its cousin garlic mustard. Both are responsible for crowding out native woodland plants. I must admit that it is quite pretty when you drive by and see large swaths of pinks, purples, and whites along the wooded roadsides, but nevertheless it is bad stuff here. My neighbors apparently didn't get the message, because they planted some in their garden. My other neighbor planted goutweed. I wish garden centers would stop selling such invasive plants.

I'd surely never plant dame's rocket, but as a shade-intolerant plant, I disagree that it has anywhere near the invasive potential of garlic mustard. The two could not be more different in that regard. Let garlic mustard invade a patch of woods and even such shade-tolerant native tree types as maples can no longer germinate and grow on the forest floor. Dame's has no such ability, being confined to reasonably sunny spots. Apples and pomegranates, I'm afraid.

Thanks for the info everyone. I'll admit, it is pretty growing along the roadsides. But I'll plant something else instead. Maybe some tropical milkweed- a flower with a different controversy!! But thanks again- now I at least know what it is and some history.