As one of the essential components for flexible electronics, flexible electrochemical energy storage (EES) has garnered extensive interests at all levels of materials, devices, and systems. The successful implementation of high‐performance flexible EES devices relies on exploring of suitable electrode/electrolyte materials that have both superior electrochemical and mechanical properties. For this function, one‐dimensional electrospun nanofibers have emerged as a class of promising building blocks for the key components of flexible EES devices. In this overview, the fundamental principles and technical advances of electrospinning are examined, for both their successes and challenges in controllable fabrication of nanofibers with the desirable chemical compositions, micro/meso‐/nanostructures, and therefore resultant properties. The advances in applications of electrospun nanofibers for various key flexible EES devices are critically looked into, including those in supercapacitors, metal‐ion batteries, and metal‐air batteries. The existing challenges and prospects of these electrospun nanofiber‐based flexible EES are discussed, aiming to inspire continued efforts in developing the optimal high‐performance and low cost flexible EES devices for long‐awaited practical applications.