There is a growing demand for flexible and soft electronic devices. In particular, stretchable, skin-mountable, and wearable strain sensors are needed for several potential applications including personalized health-monitoring, human motion detection, human-machine interfaces, soft robotics, and so forth. This Feature Article presents recent advancements in the development of flexible and stretchable strain sensors. The article shows that highly stretchable strain sensors are successfully being developed by new mechanisms such as disconnection between overlapped nanomaterials, crack propagation in thin films, and tunneling effect, different from traditional strain sensing mechanisms. Strain sensing performances of recently reported strain sensors are comprehensively studied and discussed, showing that appropriate choice of composite structures as well as suitable interaction between functional nanomaterials and polymers are essential for the high performance strain sensing. Next, simulation results of piezoresistivity of stretchable strain sensors by computational models are reported. Finally, potential applications of flexible strain sensors are described. This survey reveals that flexible, skin-mountable, and wearable strain sensors have potential in diverse applications while several grand challenges have to be still overcome.