With the emergence of flexible/stretchable electronic devices, flexible supercapacitors (SCs) have attracted widespread interest in developing lightweight, thin, elastic and efficient portable/wearable energy storage devices that show promising applications in hybrid electric vehicles, uninterruptible power supplies and “smart textiles”. Along with a brief description on the general information about flexible SCs, this feature article focuses on recent advances in flexible SCs including the planar-structured flexible SCs and the new-type fiber SCs as well as fiber integrated/hybrid energy systems containing fiber SCs. The construction of efficient active materials on flexible substrates (e.g. plastics, papers, fabrics/textiles, fibrous substrates, etc.) and feasible strategies to achieve high-performance flexible SCs are highlighted. Perspectives on the research trends of flexible SCs toward practical applications are proposed.