Herbs become invasive in one of two ways. Some freely scatter their seeds, that seem to sprout with ease even in the most inhospitable conditions. Others send out rhizomes (root-like stems) that meander along just under the soil's surface; sprouting new plants as they go. Both are highly efficient ways to overrun your garden and choke out existing plants. Here are some ways to keep these invasive herbal companions in check.
If you find that one of the invasive herbs in your garden has managed to escape, dig up the unwanted seedlings, making sure to remove the entire root system. Then sift through the soil with a digging fork to make sure you get any leftover pieces. Keep an eye on the area for several months, and either dig out any plants that reappear or clip them off at soil level and smother them for several weeks with a heavy layer of newspaper or a large, flat stone.
Catalogue Clues: When shopping for herbs in garden catalogs, invasive herbs should come with a warning (mint in particular), but they usually don't, so you'll need to do your homework as well as learn to read between the lines. Plant descriptions such as 'carefree", "vigorous", "establishes quickly", or 'grows anywhere" may be code for invasive tendencies. When acquiring herbs locally, consult other gardeners, local nurseries, and your local extension agent about herbs that are invasive in your area.
By Ellen Brown

Invasive Plants And How You Can Minimize Their Spread
Do your part. As soon as you notice an invasive species on your property remove it. If you see invasive plants in your neighborhood, volunteer to help other property owners remove them.
Choose plants for your landscape wisely. The behavior of a plant can vary widely from region to region. Always check a plantís invasive reputation before adding it to your landscape. What may be loved by one gardener (e.g. trumpet vine, monkey grass) may be a huge headache when planted in your zone.
Consider using native plants or non-invasive alternatives in your landscape.
By Ellen Brown
Many plants, especially herbs, are very invasive and will spread and quickly take over your garden. To prevent this, place the plant, like this spearmint, in a container. This mint is planted inside an old ice cream maker. I have a beautiful plant and don't have to worry about it taking over!
I purchased a home that was professionally landscaped about 18 years ago but the previous owners did not maintain the beds. A ground cover called "Snow on the Mountain" was used in the largest bed and has taken over. I pulled so much of it out in the fall (including roots) that I thought I'd at least have one spot that was clear but it's back and taking over again! Does anyone have any idea how I can tame this creature? It's a beautiful ground cover so I don't want to kill it entirely but I need to control it.
Hardiness Zone: 5a
Joanne H. from Weare, NH
I have Bishop's weed (sometimes confused with Snow on the Mt). This too is an invasive weed. I was told to cover it with black plastic, use rocks to secure it and leave it for 1 year. Check to see if any little sprouts are escaping and pull them. Perhaps combined with Round Up? I do know it is very, very (darn near impossible) to get rid of.
Q: I have a problem. I have unfortunately acquired a terribly invasive weed. I have no idea what it is. It looks like a fern, has black pods along it's length, grows in clumps, prefers areas heavily mulched but basically took over large areas of my yard in late winter/early spring. For various reasons I was unable to get out and attack it when it was at its peak. It has now been sprayed and most of it is dead, but not before I'm pretty sure it went to seed, to spend time preparing for the next attack.
I would like to find a practically invasive ground cover to plant in the worst area that might inhibit, or at least challenge, this weed the next time it rears its ugly leaves. It would be great if it was evergreen and shade-loving, but at this point I'll take any suggestions. Does anyone have any ideas as to what I might use? Thanks so much!
Hardiness Zone: 8a
Tripleb from Greenville, AL
A: Tripleb,
Congratulations on getting rid of your very invasive weed. There are several options for ground covers that many people would consider "invasive." Examples include: English ivy, wintercreeper, crownvetch, ajuga, periwinkle, Liriope spicata and certain types of honeysuckle. Of these examples, wintercreeper grows wonderfully in the shade and is highly competitive with under-story plants. Lily-turf is an evergreen that quickly spreads to form a dense mat and can be used to cover a large area. It produces spikes of purple or white flowers, which eventually transform into clusters of black berries. It also provides and interesting texture and grows equally well in sun or shade. It tolerates a wide variety of soil conditions, although it prefers moist, nutrient-rich soil. All of these examples should perform well in your zone.
Good Luck!
Ellen
By Ellen Brown
I'd love a picture, kmcl! Thanks to all for the suggestions!
How do you kill snow on the mountain ground cover?
By CMills
Round up will kill it and the root system, digging it up and giving it to others would be nice but probably wouldn't get rid of root system.