They are invasive but for a change not from Asian countries, but this time from southern Switzerland southward around much of the Mediterranean basin, from Portugal to Turkey, and across much of north Africa according to www.invasivespecies.IN.gov .
They were introduced as a medicinal herb and as an ornamental ground cover.
Planting alternatives, will depend on where you live. At the IN. gov site they recommend
Dwarf Crested Iris (Iris cristata)
Palm Sedge (Carex muskingumensis)Wild Ginger (Asarum canadense)
Creeping Phlox (Phlox subulata)
But! As you and I both know, those desirables are much more difficult to become established and provide ground cover and weed prevention.