Smart textiles have not only the necessary functions of daily wear, but also the intelligence. The focus of the current textile materials research is the selection of flexible material. For flexible materials, carbon material is one of the ideal materials for preparing flexible strain gauges. The application of flexible strain sensor prepared by carbon nanotubes as a flexible material in smart textiles is the research content. The research status of carbon nanotubes flexible strain sensor is introduced from the aspects of the structure, properties and application. The characteristics and functions of flexible strain gages prepared with carbon nanotube fibers and carbon nanotube films as flexible materials are discussed in terms of selection, preparation method, performance test and application. At the same time, the advantages and disadvantages of the flexible strain sensor of carbon nanotubes are reviewed from the aspects of preparation difficulty, production cost and practical application effect. High sensitivity with high strain will be a key research direction for carbon nanotube flexible strain sensors.