During the last few decades, magnetorheological (MR) elastomers have attracted a significant amount of attention for their enormous potential in engineering applications. Because they are a solid counterpart to MR fluids, MR elastomers exhibit a unique field-dependent material property when exposed to a magnetic field, and they overcome major issues faced in magnetorheological fluids, e.g. the deposition of iron particles, sealing problems and environmental contamination. Such advantages offer great potential for designing intelligent devices to be used in various engineering fields, especially in fields that involve vibration reduction and isolation. This paper presents a state of the art review on the recent progress of MR elastomer technology, with special emphasis on the research and development of MR elastomer devices and their applications. To keep the integrity of the knowledge, this review includes a brief introduction of MR elastomer materials and follows with a discussion of critical issues involved in designing magnetorheological elastomer devices, i.e. operation modes, coil placements and principle fundamentals. A comprehensive review has been presented on the research and development of MR elastomer devices, including vibration absorbers, vibration isolators, base isolators, sensing devices, and so on. A summary of the research on the modeling mechanical behavior for both the material and the devices is presented. Finally, the challenges and the potential facing magnetorheological elastomer technology are discussed, and suggestions have been made based on the authors' knowledge and experience.