We study the extreme amenability of topological groups, i.e., the property that every flow has a fixed point. First, we look at automorphism groups of structures, and characterize the extreme amenability in terms of the Ramsey property for the class of their finitely generated substructures. Then we apply our results to compute the universal (initial) minimal flow of the group of self-homeomorphisms of the real line.We will also discuss a result which canonically presents every flow of a separable group as an inverse limit of metrizable flows, and as a corollary we conclude that for separable groups to be extremely amenable, it suffices that every metrizable flow has a fixed point.These ideas are based on the work of Kechris, Pestov and Todorcevic in 2005.