The critical points of the length function on the free loop space L(M) of a compact Riemannian manifold M are the closed geodesics on M. Filtration by the length function gives a link between the geometry of closed geodesics and the algebraic structure given by the Chas-Sullivan loop product on the homology of L(M). Geometry reveals the existence of a related product on the cohomology of L(M). For manifolds such as standard spheres and projective spaces where all geodesics are closed, the resulting homology and cohomology rings are nontrivial, and closely linked to the geometry. (I will not assume any knowledge of the Chas-Sullivan product.) Joint work with Mark Goresky.