The attention given to magnetorheological elastomers (MREs) has been on the rise over the last few decades. MREs feature a remarkable field-controllable modulus or mechanical characteristics that are influenced by an external magnetic field. Compared to its family member magnetorheological fluids (MRF), MREs offer advantages in terms of overcoming sealing and sedimentation issues. This makes them highly promising for the development of smart base isolation systems of buildings and other infrastructures. This review paper attempts to highlight the impactful progress of MRE base isolation in civil engineering over the past decades. It begins with a brief introduction of MREs including its fundamental principles, operation modes, and fabrication process. Then, the recent investigations of MREs and MRE base isolators are reviewed. Finally, discussions are made on the challenges and potential topics for further investigations.