Abstract: The story begins with Urysohn's universal complete separable metric space and its remarkably rich isometry group (1924), and a fundamental combinatorial theorem due to Ramsey (1930). The threads come together with the realization that the topological dynamics of Urysohn's isometry group depend on a far reaching generalization of Ramsey's theorem, as was shown by Kechris, Pestov, and Todorcevic (2005). This surprising connection has sent me back to some unfinished business of my own in model theory, with a fresh perspective. I will explain the model theoretic and topological issues, and the combinatorics that links them, and talk about my current projects on the model theoretic side of the picture.