With the rapid development of medicine in contemporary society, wearable and flexible healthcare devices will attract great attention as emerging medical electronics. Flexible and stretchable sensors, as an important component of many wearable healthcare devices, will allow real-time monitoring of daily health data for diagnosis and prediction of early stages of diseases, providing a great boost to modern medicine. This paper reviews the development of wearable flexible sensors and the latest research progress, including flexible sensors based on conductive nanocomposite hydrogels, graphene, and Janus membranes, analyzes the principles and characteristics of flexible sensors of different technological routes, and discusses the challenges and opportunities of flexible sensors. Achieving accurate real-time data transmission and analysis for flexible sensors, as well as low power consumption, is a major challenge. Flexible sensors will become increasingly important in personalised medicine, health monitoring, non-invasive diagnostics and telemedicine. They will be a tool for more convenient, accurate and efficient health management.