The Procrustes-Wasserstein problem consists in matching two high-dimensional point clouds in an unsupervised setting, and has many applications in natural language processing and computer vision. We consider a planted model with two datasets X, Y that consist of n datapoints in R^d, where Y is a noisy version of X, up to an orthogonal transformation and a relabeling of the data points. This setting is related to the graph alignment problem in geometric models. For this problem, I will take the euclidean transport cost between the point clouds as a measure of performance for the alignment. We will first discuss some information-theoretic results, in the high (d≫logn) and low (d≪logn) dimensional regimes. Then, we will talk about computational aspects and introduce the Ping-Pong algorithm, alternatively estimating the orthogonal transformation and the relabeling.