Magnetorheological fluids (MRFs) are classified as intelligent materials whose rheological and mechanical properties can be modified by interaction with an external magnetic field. These unique features allow for a controlled change of their viscosity, which is applied in technology to build adaptive devices and effectively suppress vibrations in various mechanical systems. In this paper, we overview and discuss our previous results regarding advances and physicochemical MRF properties in the context of broader literature. We concentrated on such properties as flow, yield strength, and viscoelastic behavior under shearing flows. We briefly discussed continuum and discrete MRFs modeling. Since the magnetic core is mainly based on iron or its compounds, depending on its chemical composition, morphology, stabilizing agents, and the liquid medium’s viscosity, its rheological and micromechanical properties can be moderated. To predict the behavior of such a fluid, it is necessary to propose and implement an appropriate model. Simple models like Bingham can consider the quasi-static and dynamic behavior of the MRFs, while discrete models are applied to the development and implementation of the MRF control algorithms. Thus, analytical and numerical simulation compromise the accuracy, quantity of considered phenomena, and computational cost.