Magnetorheological (MR) material started to gain exposure when researchers explore the potential of magnetic field-responsive material based on fluid (MRF), foam (MR foam), elastomer (MRE), and gel (MRG). Magnetorheological elastomer (MRE) is a smart material in which its physical properties can be changed rapidly and reversibly under varying magnetic field strength. Due to the potential commercialization of MRE-based devices, the fundamental factors that affect the rheological and mechanical properties of MRE need to be identified and documented properly. Various factors such as ferromagnetic particles' condition, elastomer matrix's condition, strain amplitude, exciting frequency, temperature, and many more have been reviewed and presented with supporting figures highlighting the MRE's current findings. A collection of MRE-based devices is also presented to summarize the applications explored by current researchers. A few challenges in the MRE research require immediate attention. It includes designing an innovative MRE fabrication equipment incorporating an electromagnet to permit anisotropic particle configuration during crosslinking. Moreover, an optimum thickness of MRE needs to be studied in every MRE-based device design to ensure that the magnetic field is optimized thoroughly. Therefore, more studies ought to be done to improve the MRE that can enable the commercialization of MRE in various applications. © 2021 The Author(s)