In this talk, I will present different ways of conducting principal component analysis of datasets whose elements are probability distributions. For that purpose, I will consider the pseudo-Riemannian structure of the space of probability distributions (with moments of order 2) endowed with the Wasserstein metric. The nice geometric properties (such as the existence of geodesics) of the Wasserstein space do not, however, allow applying classical statistical learning tools such as PCA for Hilbert spaces. Using techniques borrowed from Riemannian geometry or redefining projections are all tools to produce a meaningful second order statistical analysis of a dataset of probability measures.