In this thesis, we study some dynamical and geometrical properties of the geodesic flow of certain compact manifolds without conjugate points. The thesis has two main parts. We first extend Gelfert-Ruggiero s work about the existence of an expansive factor for the geodesic flow to the case of compact surfaces without conjugate points and genus greater than one. The main idea is to define an equivalence relation that collapses biasymptotic orbits of the geodesic flow. This induces a factor time-preserving semi-conjugate to the geodesic flow under the quotient map. Moreover, the factor is expansive, topologically mixing and has a local product structure. These properties imply that the factor has a unique measure of maximal entropy. We lift this measure to the unit tangent bundle and make sure that it is the unique measure of maximal entropy for the geodesic flow. This provides an alternative proof of Climenhaga-Knieper-War’s theorem for the uniqueness result. In the last part of the thesis, we extend some results of Gelfert and Ruggiero from compact higher genus surfaces without conjugate points to compact n-manifolds without conjugate points and Gromov hyperbolic universal covering. Assuming that Green bundles are continuous and the existence of a hyperbolic closed geodesic, we show that Green bundles are tangent to the horospherical foliations. Moreover, the horospherical foliations are the only continuous foliations of the unit tangent bundle, invariant by the geodesic flow and satisfying a condition of local transversality. This fact was only known for compact surfaces without conjugate points by Barbosa-Ruggiero s work, and in higher dimensions assuming the stronger condition of bounded asymptote by Eschenburg s work.