Magnetically actuated microrobots have become a research hotspot in recent years due to their tiny size, untethered control, and rapid response capability. Moreover, an increasing number of researchers are applying them for micro-/nano-manipulation in the biomedical field. This survey provides a comprehensive overview of the recent developments in magnetic microrobots, focusing on materials, propulsion mechanisms, design strategies, fabrication techniques, and diverse micro-/nano-manipulation applications. The exploration of magnetic materials, biosafety considerations, and propulsion methods serves as a foundation for the diverse designs discussed in this review. The paper delves into the design categories, encompassing helical, surface, ciliary, scaffold, and biohybrid microrobots, with each demonstrating unique capabilities. Furthermore, various fabrication techniques, including direct laser writing, glancing angle deposition, biotemplating synthesis, template-assisted electrochemical deposition, and magnetic self-assembly, are examined owing to their contributions to the realization of magnetic microrobots. The potential impact of magnetic microrobots across multidisciplinary domains is presented through various application areas, such as drug delivery, minimally invasive surgery, cell manipulation, and environmental remediation. This review highlights a comprehensive summary of the current challenges, hurdles to overcome, and future directions in magnetic microrobot research across different fields.