2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/57439This paper is a review of recent and classical results on integrable geodesic flows on Riemannian manifolds and topological obstructions to integrability. We also discuss some open problems.37 pagesMathematical PhysicsDynamical SystemsExactly Solvable and Integrable Systems70H06, 37J35, 53D17, 53D25Integrable geodesic flows on Riemannian manifolds: Construction and Obstructionstext