Abstract: The representation type of a quiver Q can be characterized by the geometric properties of the associated quiver Grassmannians: (a) Q is representation finite if all quiver Grassmannians are smooth and have cell decompositions into affine spaces; (b) Q is tame if all quiver Grassmannians have cell decompositions into affine spaces and if there exist singular quiver Grassmannians; (c) Q is wild if every projective variety occurs as a quiver Grassmannian. With the exception of (extended) Dynkin type E, this result is proven in joint work with Thorsten Weist, based on previous results by Haupt, Reineke, Hille and Ringel. The result for type E is