With the serious impact of fossil fuels on the environment and the rapid development of the global economy, the development of clean and usable energy storage devices has become one of the most important themes of sustainable development in the world today. Supercapacitors, known as ultracapacitors, have been supposed to be one of the most promising candidates to meet the requirements of human sustainable development, due to their advantages such as high capacity, high power density, high charging/discharging speed, long cycle life, and low processing cost. However, the low energy density of supercapacitors limits their large-scale application. Therefore, it is of great significance to develop high energy density supercapacitors and use them as power sources for practical devices. Conductive polymer-based electrode materials have unique advantages such as high theoretical capacitance, good conductivity, and good flexibility, and have high potential in supercapacitors. The research on conductive polymer-based electrode materials has promoted the rapid development of the field of supercapacitors. This review summarizes recent research progress on conductive polymers (including polypyrrole, polyaniline, and polythiophene), conductive polymer-based binary composites, and conductive polymer-based ternary and quaternary composites for supercapacitor electrodes. Furthermore, a summary of the use of conductive polymer-based textiles and fibers for flexible supercapacitors is also presented, along with the current challenges and future perspectives for conductive polymer-based supercapacitors.