Given a topological group G, a G-flow is a jointly continuous action GxX --> X, where X is compact Hausdorff. In particular, each topological group has a unique universal minimal flow, the "largest" minimal flow in a sense to be made precise. Unfortunately, this flow is in general not easy to construct.

Kechris, Pestov, and Todorcevic came up with a general method to compute the universal minimal flows of several automorphism groups of Fraisse structures. I will discuss this method, focusing on applications to amenability and unique ergodicity of topological groups. In particular, I will address the extent to which we can think of a Fraisse structure as a "random" expansion of a structure in a smaller language.