Over the recent years deterministic interacting-particle approximations of gradient flows in Wasserstein and other geometries have gained popularity in applications to machine learning and other areas due to their simplicity and flexibility. In these lectures we will consider various gradient flows that evolve an initial measure towards the desired target measure, which is the basic problem of variational inference. In particular we will consider the blob regularization of the Fokker-Planck equation, Stein Variational Gradient Descent, gradient flow of Maximum Mean Discrepancy, birth-death dynamics and the new Radon-Wasserstein gradient flows. In investigating the flows we will discuss which flows and which metrics are suitable in high dimensions. This is turn motivates discussing the Sliced Wasserstein metric and some related metrics.