Do you want to blow your mind?
Oh yeah I knew you did!
Go read up on the Matrioshka Brain: http://en.wikipedia.org/wiki/Matrioshka_Brain
Such a structure would be composed of a collection of one or more (typically more) Dyson spheres built around a star, and nested one inside another. A significant percentage of the shells would be composed of nanoscale computers (see molecular-scale computronium).
This plays an integral role in the book I'm currently reading, Accelerando by Charles Stross.