Electrospun nanofibers have become an important component in fabricating flexible electronic devices because of their permeability, flexibility, stretchability, and conformability to three-dimensional curved surfaces. This review delves into the advancements in adaptable and flexible electronic devices using electrospun nanofibers as the substrates and explores their diverse and innovative applications. The primary development of key substrates for flexible devices is summarized. After briefly discussing the principle of electrospinning, process parameters that affect electrospinning, and two major electrospinning techniques (i.e., single-fluid electrospinning and multifluid electrospinning), the review shines a spotlight on the recent breakthroughs in multifunctional and stretchable electronic devices that are based on electrospun substrates. These advancements include flexible sensors, flexible energy harvesting and storage devices, flexible accessories for electronic devices, and flexible environmental monitoring devices. In particular, the review outlines the challenges and potential solutions of developing electrospun nanofibers for flexible electronic devices, including overcoming the incompatibility of multiple interfaces, developing 3D microstructure sensor arrays with gradient geometry for various imperceptible on-skin devices, etc. This review may provide a comprehensive understanding of the rational design of application-oriented flexible electronic devices based on electrospun nanofibers.