If there is one hardy, shade-loving plant to grow under trees, it is arguably the hosta.
For a splash of perennial color under your trees, lilies can work well
Wild ginger (not the edible variety) actually burns in the sun, so shade is its friend.
Moist shady locations are ideal habitats for bellwort plants.
Shooting stars grow in a range of colors.
Crocuses thrive under trees because they bloom before trees leaf out.
Shady trees provide the perfect growing space for the pretty and popular periwinkle.
As plants that love the forest floor, ferns are ideally suited to life under trees.
Once they're in the ground, violets will take care of themselves.