As a new energy storage device, lithium-sulfur battery (LSB) has a sulfur cathode with a much higher theoretical specific capacity (1675 mAh g−1) and energy density (2600 Wh kg−1) compared with current lithium-ion batteries, making it a promising candidate for the next generation of energy storage devices. In recent years, the emergence of wearable electronic devices and smart textiles has placed a new demand on energy storage batteries - flexibility. Carbon materials, namely carbon fibers and several carbon nanomaterials (such as carbon nanotubes, graphene, carbon nanofibers, porous carbon skeletons, and their derivatives) possess remarkable structural and functional adjustability, and are thus well suited for building components of flexible LSBs. These components include current collectors, interlayers, solid electrolytes and anodes. This paper systematically reviews research progress in carbon materials used in different components of flexible LSBs, including the sulfur cathode, interlayer, lithium anode, and dual-functional host carbon materials that can be used as both cathode and anode. Additionally, the relationship between the processing and modification methods and the carbon materials’ structure, flexibility, and electrochemical properties is described. Finally, the problems of flexible LSBs based on carbon materials are analyzed, and the future development trend is delineated, in a part, respectively.