The purpose of the present memoir is to present a survey of my work since January 2007. The corresponding material is located at one of the intersection points between combinatorics, topological dynamics and logic via the framework of ultrahomogeneous structures and Fraïssé theory. This area has recently known a considerable expansion thanks to two major contributions by Kechris, Pestov and Todorcevic, and by Kechris and Rosendal. My work elaborates on the former and concentrates on two themes: structural Ramsey theory and topological dynamics of Polish transformation groups.
