In this talk, we will present the twisted dynamical zeta functions of Selberg and Ruelle for compact odd dimensional hyperbolic manifolds, associated with a non-unitary representation of the fundamental group. In addition, we will present the refined analytic torsion, as it is introduced by Braverman and Kappeler, and the links to the Ruelle zeta function.
We will present also the Cappell-Miller torsion and how it is related to the previous topics in the framework of the Fried's conjecture. If time permits, we will present the twisted dynamical zeta functions for all locally symmetric spaces of rank 1.