Flexible energy-storage devices increasingly attract attention owing to their advantages of providing lightweight, portable, wearable, or implantable capabilities. Many efforts are made to explore the structures and fabrication processes of flexible energy-storage devices for commercialization. Here, the most recent advances in flexible energy-storage devices based on graphene, graphene oxide (GO), and carbon nanotubes (CNTs), are described, including flexible supercapacitors and batteries. First, properties, synthesis methods, and possible applications of those carbon-based materials are described. Then, the development of carbon-nanotube-based flexible supercapacitors, graphene/graphene-oxide-based flexible supercapacitors, and graphene-and carbon-nanotube-based flexible battery electrodes are discussed. Finally, the future trends and perspectives in the development of flexible energy-storage devices are highlighted.