Tree of Heaven
Ailanthus altissima (Wikipedia, USDA, GoBotany, IPANE, USFS Weed of the Week!) is a rapidly growing medium sized tree, up to 80ft. in height. It has large compound leaves, which resemble those of sumac but have a distinctive notch and an "eye" (gland) on each side at the base of the leaf. All parts of the tree smell like peanut butter.
It spreads by seed and also aggressively by root rhizome. It produces toxins which prevent the establishment of other species.
Removal
Larger trees should be girded. If cut, the root system will respond vigorously, by both sprouting at the stump and by sending up saplings from rhyzomes. After removal, expect an overwhelming surge in Tree of Heaven saplings in the area, and both the seed bank and the rhizome system react to the increased light. Repeated years of pulling will be needed to clear the area.
Smaller saplings should be pulled, with as much of the root structure as can be found.
Common Mis-identifications
Smooth Sumac (Rhus Glabra, Wikipedia, USDA, GoBotany) and Staghorn Sumac (Rhus typhina, Wikipedia, USDA, GoBotany) have a compound leaf and juvenile growth form similar to Tree of Heaven. The difference is in the leaf detail (Sumac leaves are smooth at the base) and smell (Sumac does NOT smell like peanut butter).
Black Walnut (Juglans Nigra, Wikipedia, USDA, GoBotany) also has a similar compound leaf. The difference is that the Black Walnut leaves don't have the notch and "eye" at the base.