Magneto-/ electro-responsive polymers (MERPs) are a class of stimuli-responsive materials that are actuated when triggered by external magnetic/ electric fields. MERPs exhibit rapid, reversible, and safe multi-functional and dynamic (i.e., changing with time) properties, which can effectively be manipulated at different length scales. These features make MERPs very attractive particularly in biomedical engineering (e.g., drug delivery systems and tissue engineering), soft matter engineering (e.g., soft robotics), and structural design of smart materials with unprecedented properties (e.g., complex shape morphing). Due to the recent progress in the design and development of MERPs, here, we highlighted the current advances in fabricating MERPs using various manufacturing methods including 3D/ 4D printing and conventional techniques. We also summarized the methods used for the characterization of MERPs and discussed their important structure-property relationship. We also highlighted the potential applications of MERPs in biomedical engineering, soft robotic, and the design of smart materials and systems. MERPs show great potentials for creating smart materials with predictable dynamic properties. More studies are necessary to investigate the biological responses of MERP both in-vivo and in-vitro, which is essential for biomedical engineering applications.