State-of-the-art biomedical applications such as targeted drug delivery and laparoscopic surgery are extremely challenging because of the small length scales, the requirements of wireless manipulation, operational accuracy, and precise localization. In this regard, miniaturized magnetic soft robotic swimmers (MSRS) are attractive candidates since they offer a contactless mode of operation for precise path maneuvering. Inspired by nature, researchers have designed these small-scale intelligent machines to demonstrate enhanced swimming performance through viscous fluidic media using different modes of propulsion. In this review paper, we identify and classify nature-inspired basic swimming modes that have been optimized over large evolutionary timescales. For example, ciliary swimmers like Paramecium and Coleps are covered with tiny hairlike filaments (cilia) that beat rhythmically using coordinated wave movements for propulsion and to gather food. Undulatory swimmers such as spermatozoa and midge larvae use traveling body waves to push the surrounding fluid for effective propulsion through highly viscous environments. Helical swimmers like bacteria rotate their slender whiskers (flagella) for locomotion through stagnant viscid fluids. Essentially, all the three modes of swimming employ nonreciprocal motion to achieve spatial asymmetry. We provide a mechanistic understanding of magnetic-field-induced spatiotemporal symmetry-breaking principles adopted by MSRS for the effective propulsion at such small length scales. Furthermore, theoretical and computational tools that can precisely predict the magnetically driven large deformation fluid–structure interaction of these MSRS are discussed. Here, we present a holistic descriptive review of the recent developments in these smart material systems covering the wide spectrum of their fabrication techniques, nature-inspired design, biomedical applications, swimming strategies, magnetic actuation, and modeling approaches. Finally, we present the future prospects of these promising material systems. Specifically, synchronous tracking and noninvasive imaging of these external agents during in vivo clinical applications still remains a daunting task. Furthermore, their experimental demonstrations have mostly been limited to in vitro and ex vivo phantom models where the dynamics of the testing conditions are quite different compared the in vivo conditions. Additionally, multi-shape morphing and multi-stimuli-responsive modalities of these active structures demand further advancements in 4D printing avenues. Their multi-state configuration as an active solid-fluid continuum would require the development of multi-scale models. Eventually, adding multiple levels of intelligence would enhance their adaptivity, functionalities, and reliability during critical biomedical applications.