Magnetorheological (MR) fluids are capable of manifesting a rheological behaviour change by means of a magnetic field application and can be employed in many complex systems in many technical fields. One successful example is their use in the development of dampers: magnetorheological dampers (MRDs) are widespread in vibration control systems, as well as civil engineering applications (i.e., earthquake or seismic protection), impact absorption and vibration isolation technology in industrial engineering, and advanced prosthetics in biomedical fields. In the past, many studies have been conducted on MRDs modeling and characterization, but they have usually been focused more on the theoretical models than on the experimental issues. In this work, an overview of both of them is proposed. In particular, after an introduction to the physics of the magnetorheological effect, a short review of the main mathematical models of MRDs is proposed. Finally, in the second part of this study an overview of the main issues that occur in MRDs experimental characterization is reported and discussed.