We discuss the history of Baumgartner's result that all \aleph_1-dense sets of reals can be order-isomorphic, as well as related results of Shelah and Abraham. We'll outline a proof, due to Todorcevic, that is simpler than Baumgartner's original argument. Finally, we present some recent results of Justin Moore concerning the problem of making all \aleph_2-dense sets of reals isomorphic.