Abstract: We intend to prove the existence of at least one closed geodesic on every compact Riemannian orbifold, using methods developed in symplectic topology for proving the Weinstein conjecture. We also study orbifolds all of whose geodesics are closed with the help of holomorphic curve techniques. A further aim is to understand the topology of highly connected orbifolds, with applications to Riemannian foliations on manifolds.