Many algorithms for statistical inference can be fruitfully studied as Wasserstein gradient flows, but in order to develop useful algorithms, we must develop efficient implementations. Famously, the Wasserstein gradient flow of the KL divergence can be realized via the Langevin diffusion, which is widely used as an algorithm for sampling. I will discuss an alternative implementation called the proximal sampler, which takes inspiration from the proximal point method from convex optimization. I will also briefly discuss applications of Wasserstein gradient flows to variational inference.