Advances in flexible and stretchable electronics, functional nanomaterials, and micro/nano manufacturing have been made in recent years. These advances have accelerated the development of wearable sensors. Wearable sensors, with excellent flexibility, stretchability, durability, and sensitivity, have attractive application prospects in the next generation of personal devices for chronic disease care. Flexible and stretchable wearable sensors play an important role in endowing chronic disease care systems with the capability of long-term and real-time tracking of biomedical signals. These signals are closely associated with human body chronic conditions, such as heart rate, wrist/neck pulse, blood pressure, body temperature, and biofluids information. Monitoring these signals with wearable sensors provides a convenient and non-invasive way for chronic disease diagnoses and health monitoring. In this review, the applications of wearable sensors in chronic disease care are introduced. In addition, this review exploits a comprehensive investigation of requirements for flexibility and stretchability, and methods of nano-based enhancement. Furthermore, recent progress in wearable sensors-including pressure, strain, electrophysiological, electrochemical, temperature, and multifunctional sensors-is presented. Finally, opening research challenges and future directions of flexible and stretchable sensors are discussed.