I will report on joint work with Dolors Herbera. We study the
representation type of a hereditary, indecomposable, left pure
semisimple ring in terms of properties of a certain tilting and
cotilting module W. In particular, we apply the tilting and the
cotilting functors to describe the Auslander-Reiten-components of the
endomorphism ring of W. I will close the talk with a list of open
questions.