<p>Magnetic soft continuum robots (MSCRs) integrate remote and untethered actuation capability and inherent biocompatible nature of magnetic fields with the compliance of soft components, holding significant potential in biomedical applications. Among various MSCRs, hard-magnetic soft continuum robots (hMSCRs), leveraging materials with hard-magnetic properties, have attracted increasing attention due to their programmable magnetization and large reversible deformations. This review summarizes recent progress in hMSCRs, focusing on the modeling, design, and biomedical applications. First, we introduce fundamental characteristics, actuation mechanisms, and constitutive modeling frameworks of hard-magnetic soft materials. Then, we discuss several typical static and dynamic modeling approaches for two primary categories of hMSCRs: permanent magnet-based and magnetic particle-based systems. Next, design strategies emphasizing structural versatility and functionality are then presented for both types of hMSCRs. Finally, representative biomedical applications in navigation and endoscopy are highlighted, underscoring the transformative potential of hMSCR technologies in clinical practice.</p>