Follow this link to learn how to spot the two types of invasive buckthorn in the state…
Common and Glossy Buckthorn are the two types of invasive non-native buckthorn found in Minnesota. The ends of most Common Buckthorn branches have a thorn that is hugged (set in between) either two buds or two leaves. The combination of buds and thorn look similar to a deer's hoof (the "buck" in buckthorn). Glossy Buckthorn, the other non-native invasive buckthorn, can be a little trickier to identify, but often has a distinctly tall columnar shape (shaped like a column).
Both Common and Glossy Buckthorn are easier to identify in the late fall. They tend to hold their leaves longer than other shrubs. If you look out into the woods and see most trees and shrubs have lost their leaves, but there is a bunch of one type of shrub that is still leafy green, it is probably Buckthorn.
The Midwest Invasive Species Information Network offers two great quick training modules on the identification of Common and Glossy Buckthorn at http://www.misin.msu.edu/training/.