Radar-based non-contact health monitoring technology (RBNHMT) has emerged as a transformative paradigm in continuous health sensing, enabling non-invasive and continuous monitoring of physiological parameters and behavioral patterns by transmitting electromagnetic waves, analyzing the reflected signals, and detecting subtle bodily movements—ranging from millimeter-scale chest wall displacements due to respiration to micro-scale vibrations associated with cardiac activity—ultimately transforming them into quantifiable health data. Distinguished by its non-contact operation, inherent privacy preservation, and adaptability to diverse scenarios, RBNHMT exhibits stronger resistance to environmental interference than conventional contact-based monitoring, and has solidified its position as a prominent and dynamic research focus in the field of non-contact health monitoring. Currently, significant and multifaceted progress has been made across several key areas. In human activity recognition (HAR), systems leveraging micro-Doppler signatures or point cloud sequences realize high-precision detection of gait, gestures, and fall events, with state-of-the-art deep learning-based models achieving accuracy rates exceeding 99% in controlled experimental settings. For vital sign and sleep monitoring, it not only tracks respiratory and heart rates continuously but also extracts clinically relevant metrics such as heart rate variability (HRV) for autonomic nervous system assessment and estimates blood pressure through indirect methods like pulse transit time analysis, maintaining robustness in dynamic settings through advanced motion compensation algorithms. In sleep monitoring, it further enables sleep posture classification and apnea event detection. In emotion and stress recognition, it provides a non-intrusive approach for psychological assessment by analyzing autonomic-response physiological signal patterns or behavioral features. Furthermore, its applications in auxiliary medical diagnosis have expanded to promising interdisciplinary areas such as non-contact heart sound auscultation, radar-based screening for obstructive sleep apnea (OSA), and emerging research into breast cancer detection using microwave and millimeter-wave imaging techniques. However, several challenges impede its practical deployment. Signal quality is significantly compromised by multipath interference in complex indoor environments and clutter from static objects, and by motion artifacts in dynamic scenarios where gross body movements obscure the subtle physiological signals. Algorithmically, separating signals from multiple targets in close proximity and calibrating for substantial individual physiological differences, such as body habitus, baseline vital signs, remain difficult and limit generalizability. Hardware design also faces the challenge of balancing power consumption, cost, integration, and performance, often requiring trade-offs that constrain miniaturization, battery life, or measurement sensitivity. Future advancement, therefore, requires collaborative and targeted innovation across multiple dimensions. Algorithmically, developing adaptive signal processing models based on emerging paradigms like few-shot learning (for user-specific calibration with minimal data) and reinforcement learning (for dynamic noise suppression) is essential. At the hardware level, highly integrated radar SoCs with embedded processing capabilities and advanced packaging technologies such are crucial for achieving the dual goals of device miniaturization and cost reduction without sacrificing performance. At the system level, fusing radar data with complementary modalities such as infrared and acoustic sensing can create a synergistic, multi-modal framework that significantly enhances perceptual robustness and reliability in complex, real-world environments. This review provides a comprehensive synthesis that systematically summarizes relevant theoretical foundations and application progress, and offers an in-depth analysis of current technical bottlenecks. It aims to provide a clear development path and a foundational academic reference for the in-depth integration and practical application of RBNHMT in critical scenarios including rehabilitation engineering, smart elderly care, in-vehicle health monitoring, and beyond, thereby offering innovative technical support for the vision of universal, proactive, and personalized health management.