In the previous chapter, we developed a Riemannian structure on the space \((\mathcal {P}_2(\mathbb {R}^d), W_2)\) in order to define Wasserstein and WFR gradient flows. In this chapter, we use these gradient flows as optimization algorithms over the space of probability measures for various tasks arising in statistics and machine learning. Each task corresponds to choosing a specific functional \(\mathcal {F}\) over this space. In particular, akin to the notion of convexity in classical optimization (see, e.g., [56]), the notion of geodesic convexity is instrumental in deriving rates of convergence.