Shady places can drive gardeners crazy. Sometimes we just want to cover them with something, anything, that will grow. That might have been what that long-ago colonial gardener was thinking when she brought to North America the shade-loving goutweed (Aegopodium podagraria). Deep green three-parted and three-parted-again foliage, airy white flower clusters on strong three-foot stems, pest-free and quickly spreading where nothing else will survive: what more could one ask for?
A little less of a good thing, for one. Goutweed was already well-established in North America by the time of the Civil War, and now, in the Northeast, at least, it is hugely common. Like most invasive plants, it prefers disturbed areas - but then what isn't disturbed in our lived-in landscapes? Shady roadsides, gardens, backyards, streambanks - they're all likely locations for goutweed.
Goutweed is highly rhizomatous, that is, with shoot-producing running underground stems. And that is how patches increase in size, by spreading of the long, white, mat-forming rhizomes. Gardeners who have goutweed in their landscapes know how luxuriously these rhizomes can grow - from the compost pile or the weed heap. Goutweed doesn't produce a lot of seeds, and those are short-lived. Instead, it is a camp-follower, spread by people who unknowingly move about pieces of rhizomes in compost or yard waste. It happens often enough that Vermont's Invasive Exotic Plant Committee lists it as a Category 1 plant, one that is highly invasive and which is currently displacing native plants. (This applies only to the species itself, not the variegated cultivars. They are much less vigorous, or so it seems at present.)
Some sources say goutweed can be controlled by hand-pulling, but you must be retired to have the time for it! Frequent mowing might eventually do the plant in. Herbicides certainly will. But an environmentally friendly control method is to simply deprive the pesky patch of light, early in the season when all its energies are programmed toward foliage production. Cover the patch of goutweed with black plastic or cardboard or landscape fabric (and cover that item with hay or straw to improve its looks). Leave the barrier on for the entire growing season.
Then next year, plant there something shade-loving but well-behaved. A number of native plants - think of ferns, for example - will do the green thing quite politely.