  We present problems and results that combine graph-minors and coarse
geometry. For example, we ask whether every geodesic metric space (or graph)
without a fat $H$ minor is quasi-isometric to a graph with no $H$ minor, for an
arbitrary finite graph $H$. We answer this affirmatively for a few small $H$.
We also present a metric analogue of Menger's theorem and Konig's ray theorem.
We conjecture metric analogues of the Erdos--Posa Theorem and Halin's grid
theorem.
