Supercapacitors are a highly promising class of energy storage devices due to their high power density and long life cycle. Conducting polymers (CPs) and organic molecules are potential candidates for improving supercapacitor electrodes due to their low cost, large specific pseudocapacitance and facile synthesis methods. Graphene, with its unique two-dimensional structure, shows high electrical conductivity, large specific surface area and outstanding mechanical properties, which makes it an excellent material for lithium ion batteries, fuel cells and supercapacitors. The combination of CPs and graphene as electrode material is expected to boost the properties of supercapacitors. In this review, we summarize recent reports on three different CP/graphene composites as electrode materials for supercapacitors, discussing synthesis and electrochemical performance. Novel flexible and wearable devices based on CP/graphene composites are introduced and discussed, with an eye to recent developments and challenges for future research directions.