The fiber grating sensor has the advantages of light weight, small size, high sensitivity, strong anti-electromagnetic interference capability and so on, especially good flexibility and compatibility. The fiber grating and flexible materials can be fabricated into a flexible sensor with high-density distributed perception by means of the special preparation technology. The basic sensing principles of fiber grating were introduced; then the fiber grating flexible sensors using silicone rubber, textile and other polymers as the substrates were introduced in detail, and the preparation technologies, structural characteristics and performance of various flexible sensors were analyzed; finally, the main problems, application fields and future research directions of flexible sensors were discussed.