We describe a striking connection between Arnold's least-action principle for incompressible Euler flows and geodesic paths for Wasserstein distance. The least-action problem for geodesic distance on the `manifold' of fluid-blob shapes exhibits instability due to microdroplet formation. A connection with fluid mixture models via a variant of Brenier's relaxed least-action principle for generalized Euler flows will be outlined also. This is joint work with Bob Pego and Dejan Slepcev. Speaker(s): Jian-Guo Liu (Duke Univ.)