Medical time series data often exhibit intricate and dynamic patterns. With the rapid advancement of medical digitization, deep learning-based time series anomaly detection techniques have found extensive applications in the healthcare field, such as detecting irregular heart rhythms and monitoring patients' vital signs. By reviewing and summarizing the relevant research, this paper explores the deep learning-based time series anomaly detection techniques within the medical and health domain, analyzing the strengths and limitations of different deep learning architectures and algorithms in tackling specific medical tasks. Lastly, we discuss the challenges faced by this field and outline future research directions.