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The topic of this paper is the identification of a high-precision model for Magneto-Rheological (MR) dampers. A semi-active MR-damper can be seen as a non-linear system, where the inputs are the stroke-velocity and the command current; the current is the control input which modulates at high-bandwidth the damping characteristic through the variation of a magnetic field. The output is the force delivered by the damper. Among the broad set of applications where MR-dampers can be used, this work mainly focuses on MR-dampers for the control of vehicle dynamics (trains, road vehicles, tractors, etc.). High-precision models of MR dampers can be designed using two different model classes: gray-box models (also called semi-physical models) and black-box models. Both approaches are considered in this work.