Polyaniline materials are widely utilized as electrodes for supercapacitors because of low cost, facile synthesis, high mechanical flexibility and theoretical high specific capacitance. However, the poor cycle stability and low rate capability restrict their practical applications. Integration of polyaniline with carbon materials is an effective strategy to solve the aforementioned limitations. In this review, polyaniline electrode materials, especially in the forms of different nanostructures, are firstly summarized to demonstrate the general merits of polyaniline-carbon composites for supercapacitors. Subsequent emphasis focuses on the rational design of the composites with various carbon materials, including activated carbon, porous carbon, carbon nanotubes, carbon fibers, graphene or their hybrids. The importance of the compositions, desired architectures and synergistic interactions on the enhanced electrochemical properties is emphasized. In particular, the research trends in the configurational design of unconventional devices, such as flexible, stretchable, compressible and asymmetric supercapacitors with excellent performance at different states (bending, stretching, compressing and/or folding). The review ends with a summary and discusses the perspectives and challenging issues regarding the rational design of flexible supercapacitors in future studies, along with the current outlook for the integrated electronic devices.