The unprecedented non-contact, non-invasive, and privacy-preserving nature of radar sensors has enabled various healthcare applications, including vital sign monitoring, fall detection, gait analysis, activity recognition, fitness evaluation, and sleep monitoring. Machine learning (ML) is revolutionizing every domain, with radar-based healthcare being no exception. Progress in the field of healthcare radars and ML is complementing the existing radar-based healthcare industry. This article provides an overview of ML usage for two major healthcare applications: vital sign monitoring and activity recognition. Vital sign monitoring is the most promising healthcare application of radar, as it can predict several chronic cardiac and respiratory diseases. Activity recognition is also a prominent application since the inability to perform activities may result in critical suffering. The article presents an overview of commercial radars, radar hardware, and historical progress of healthcare radars, followed by the usage of ML for healthcare radars. Subsequently, the paper discusses how ML can overcome the limitations of conventional radar data processing chains for healthcare radars. The article also touches upon recent generative ML concepts used in healthcare radars. Among several interesting findings, it was discovered that ML does not completely replace existing vital sign monitoring algorithms; rather, ML is deployed to overcome the limitations of traditional algorithms. On the other hand, activity recognition always relies on ML approaches. The most widely used algorithms for both applications are Convolutional Neural Network (CNN) followed by Support Vector Machine (SVM). Generative AI has the capability to augment data and is expected to have a significant impact soon. Recent trends, lessons learned from these trends, and future directions for both healthcare applications are presented in detail. Finally, the future work section discusses a wide range of healthcare topics for humans, ranging from neonates to elderly individuals.