  We prove that if the universal minimal flow of a Polish group $G$ is
metrizable and contains a $G_\delta$ orbit $G \cdot x_0$, then it is isomorphic
to the completion of the homogeneous space $G/G_{x_0}$ and show how this result
translates naturally in terms of structural Ramsey theory. We also investigate
universal minimal proximal flows and describe concrete representations of them
in a number of examples.
