The projective shape of a configuration consists of the information that is invariant under projective transformations. It encodes the information about an object reconstructable from uncalibrated camera views. The space of projective shapes of k points in RP(d) is by definition the quotient space of k copies of RP(d) modulo the action of the projective linear group PGL(d). A detailed examination of the topology of projective shape space is given, and it is shown how to derive subsets that are differentiable Hausdorff manifolds and can be provided with a Riemannian metric. A special case are Tyler regular shapes for which a Riemannian metric is given. This is joint work with Florian Kelma (TU Ilmenau) and John T. Kent (University of Leeds).