Ground cover.

Epimediums, hellebores, for a start . . . . .

Try Waldsteinia. There are two varieties: ternata & fragariodies. Strawberry shaped leaves and yellow flowers in early summer.
Also worth a try is Pachysandra terminalis, although under trees may be a little too dry for that one.

A very usefull ground cover plant that is often overlooked is Lamium Yellow Arkangel, this is a varigated plant with silvery green yellow leaves, it has fantastic upright yellow flowers in the spring/early summer, note it is very invasive, i would say in a nice way but easily kept in check, it will brighten up shady areas all summer long, a must for any shady situation.

And on the Lamium theme that Julien introduced, I'd add Lamium maculatum 'White Nancy' or L. 'Beacon Silver'. Very attractive leaves, the first with white flowers, the second with lilac/purple.