The field of biomedical radar has witnessed significant advancements in recent years, paving the way for innovative and transformative applications in clinical settings. Most medical instruments invented to measure human activities rely on contact electrodes, causing discomfort. Thanks to its noninvasive nature, biomedical radar is particularly valuable for clinical applications. A significant portion of the review discusses improvements in radar hardware, with a focus on miniaturization, increased resolution, and enhanced sensitivity. Then, this paper also delves into the signal processing and machine learning techniques tailored for radar data. This review will explore the recent breakthroughs and applications of biomedical radar technology, shedding light on its transformative potential in shaping the future of clinical diagnostics, patient and elderly care, and healthcare innovation.