Building structures are vulnerable to the shocks caused by earthquakes. Buildings that have been destroyed by an earthquake are very detrimental in terms of material loss and mental trauma. However, technological developments now enable us to anticipate shocks from earthquakes and minimize losses. One of the technologies that has been used, and is currently being further developed, is a damping device that is fitted to the building structure. There are various types of damping devices, each with different characteristics and systems. Multiple studies on damping devices have resulted in the development of various types, such as friction dampers (FDs), tuned mass dampers (TMDs), and viscous dampers (VDs). However, studies on attenuation devices are mostly based on the type of system and can be divided into three categories, namely passive, active, and semi-active. As such, each type and system have their own advantages and disadvantages. This study investigated the efficacy of a magnetorheological (MR) damper, a viscous-type damping device with a semi-active system, in a simulation that applied the damper to the side of a building structure. Although MR dampers have been extensively used and developed as inter-story damping devices, very few studies have analyzed their models and controls even though both are equally important in controlled dampers for semi-active systems. Of the various types of models, the Bingham model is the most popular as indicated by the large number of publications available on the subject. Most models adapt the Bingham model because it is the most straightforward of all the models. Fuzzy controls are often used for MR dampers in both simulations and experiments. This review provides benefits for further investigation of building damping devices, especially semi-active damping devices that use magnetorheological fluids as working fluids. In particular, this paper provides fundamental material on modeling and control systems used in magnetorheological dampers for buildings. In fact, magnetorheological dampers are no less attractive than other damping devices, such as tuned mass dampers and other viscous dampers. Their reliability is related to the damping control, which could be turned into an interesting discussion for further investigation.