Enriques manifolds are non simply connected manifolds whose universal cover is irreducible holomorphic symplectic, and as such they are natural generalizations of Enriques surfaces. The goal of this talk is to prove the Morrison-Kawamata cone conjecture for such manifolds when the degree of the cover is prime using the analogous result (established by Amerik-Verbitsky) for their universal cover. We also verify the conjecture for the known examples having non-prime degree.