During important cellular processes such as centrosome and spindle positioning, dynein at the cortex interacts with dynamic microtubules in an apparent "end-on" fashion. It is well-established that dynein can generate forces by moving laterally along the microtubule lattice, but much less is known about dynein's interaction with dynamic microtubule ends. In this paper, we review recent in vitro experiments that show that dynein, attached to an artificial cortex, is able to capture microtubule ends, regulate microtubule dynamics and mediate the generation of pulling forces on shrinking microtubules. We further review existing ideas on the involvement of dynein-mediated cortical pulling forces in the positioning of microtubule organizing centers such as centrosomes. Recent in vitro experiments have demonstrated that cortical pulling forces in combination with pushing forces can lead to reliable centering of microtubule asters in quasi two-dimensional microfabricated chambers. In these experiments, pushing leads to slipping of microtubule ends along the chamber boundaries, resulting in an anisotropic distribution of cortical microtubule contacts that favors centering, once pulling force generators become engaged. This effect is predicted to be strongly geometry-dependent, and we therefore finally discuss ongoing efforts to repeat these experiments in three-dimensional, spherical and deformable geometries.