When I first moved to Minneapolis, I started noticing certain plants that I didn't recognize from my time in the country and outer-ring suburbs. They are probably present to some extent in those areas, but they are endemic here and in St. Paul.
When first starting out growing a native garden and taking advantage of volunteer plants, it can be hard to tell the helpful native plants from harmful invasives. This is not meant to be an all-inclusive guide, only a starting point for some of the most common invasive weeds in the area.
The definition of "weed" is fluid and hotly contested. In this case, I am using it to describe plants that were introduced from other biomes, and are widespread and aggressive growers that will displace native plants with more value to wildlife. They should be controlled where possible, and care should be taken not to spread them to uninfested areas.
All pictures are mine. Please check out the links by clicking on the plant names for much better and more thorough information.
Nightshade
Related to tomatoes and potatoes. Attractive vine with unique leaves that vary from heart-shaped to fully lobed, and multiple small purple flowers. Can get quite large given the right conditions. Gives off a strong bitter odor when cut. Entire plant, including fruit, is poisonous to humans.
Creeping purple bellflower
Probably my most hated invasive. Very pretty plant, but it is impossible to get rid of and will choke out everything else. It spreads via taproots, so you can pull it constantly and it will just grow back. When I converted a weedy, hard-to-maintain mound behind my garage into a retaining wall, a good 50% of the volume was roots from this plant. They survived years being smothered under weed fabric and gravel and have now returned with a vengeance.
Burdock
Kinda looks like rhubarb. It's not. Don't make any pies out of it.
(Unfortunately I do not have a photo of this one.)
Lambs Quarters
Another one that pops up in bare soil and disturbed dirt.
Creeping charlie
You won't win the battle against this one, but it's not THAT problematic. It grows aggressively wherever it's given the chance, but it's easy to pull and won't choke out other plants as badly as some. Member of the mint family, square stem, smells strongly when cut. Blooms with small lavender flowers in the spring and early summer.
Goutweed
Another one that is seemingly impossible to get rid of. Aggressive ground cover, loves disturbed soil, shade, sun, whatever. Gets clusters of white flowers that are similar to Queen Anne's Lace, and also comes in a variegated green and white version. Asymmetric leaves numbering one or two on each stem.