Among the different strategies available to control engineering vibrations, the semi-active contrai based on Magnetorheological (MR) dampers have become a promising technology to be used in civil engineering structures. The ability of these devices to change the stmctairal behavior without the need of large power sources is a major advantage that can be used to justify their potential application to this engineering branch. This paper reviews the basic concept of MR fluids and provides an insight of MR dampers dynamic behavior and the available numerical procedures to describe the damper response. In the first section an overview ofthe basic properties ofthe MR fluids and the fluid behavior under different flow regimes are presented. Then, a selection of numerical models to simulate MR dampers behavior will be presented based on the available literature.