During past few years, applications of untethered magnetically controlled soft robots in the biomedical operations have been extensively reported, which is attributed to the efficient locomotion gaits, digital fabrication technologies and non-contact magnetic activation of these robots. Owing to compliance of these robots and hazardless nature of penetrating magnetic field in the living tissues of the human body, the magnetically actuated soft robots are promising tools to access delicate and narrow regions of the body and perform minimally invasive disease diagnosis and treatments. The present study aims to critically review the literature on the magnetically actuated milli, micro and nanoscale soft robots. The design, manufacturing, and in vivo and in vitro applications of the magnetic soft robots are reviewed comprehensively, and superiorities and limitations of the different designs are highlighted. The theoretical analyses along with the experimental studies reported in the literature are investigated. Applications of the permanent magnets and different types of electromagnets such as paired coils and distributed ones in providing force- and torque-driven actuations are studied. Also, the effects of strength and frequency of the applied magnetic field, materials and locomotion modes on the speed, deformation and performance of the soft robots are discussed. The healthcare-oriented applications of the magnetic soft robots such as delivery of the therapeutic payloads, cell manipulation, endoscopy and cardiovascular diseases treatments are reviewed. Finally, the challenges in the manufacturing and applications of the magnetically driven soft robots are highlighted. Since this study presents a critical review of the literature along with descriptive appendices including images, brief descriptions, and video references of the most relevant magnetically actuated soft robots and electromagnets, it can be regarded as a benchmark for the researchers who aim to conduct further research in this field. (C) 2021 Elsevier Ltd. All rights reserved.