Abstract: We propose the first global accelerated gradient method for Riemannian manifolds. Toward establishing our results, we revisit Nesterov's estimate sequence technique and develop a conceptually simple alternative from first principles. We then extend our analysis to Riemannian acceleration, localizing the key difficulty into ``metric distortion.'' We control this distortion via a novel geometric inequality, which enables us to formulate and analyze global Riemannian acceleration.