I will present some results in the theory of closed geodesics. I will state (and maybe prove parts of) the famous Gromoll-Meyer theorem which implies the existence of infinitely many geometrically distinct closed geodesics on the manifold if certain topological assumptions are fulfilled. If all geodesics on a Riemannian manifold are closed several natural questions arise, is there a common period? Do they all have the same least period? I will address those and other questions.