The de Rham decomposition theorem implies that the indecomposable factors in an isometric factorization of a one-connected, complete Riemannian manifold are unique up to order. Using a "short generating set" of the fundamental group (in the sense of Gromov), one can extend this result to the case where the manifold is not simply connected. In this talk, I will review de Rham's decomposition theorem and the mentioned extension, due to Eschenburg and Heintze.