Artificial skin, also known as bioinspired electronic skin (e-skin), refers to intelligent wearable electronics that imitate the tactile sensory function of human skin and identify the detected changes in external information through different electrical signals. Flexible e-skin can achieve a wide range of functions such as accurate detection and identification of pressure, strain, and temperature, which has greatly extended their application potential in the field of healthcare monitoring and human-machine interaction (HMI). During recent years, the exploration and development of the design, construction, and performance of artificial skin has received extensive attention from researchers. With the advantages of high permeability, great ratio surface of area, and easy functional modification, electrospun nanofibers are suitable for the construction of electronic skin and further demonstrate broad application prospects in the fields of medical monitoring and HMI. Therefore, the critical review is provided to comprehensively summarize the recent advances in substrate materials, optimized fabrication techniques, response mechanisms, and related applications of the flexible electrospun nanofiber-based bio-inspired artificial skin. Finally, some current challenges and future prospects are outlined and discussed, and we hope that this review will help researchers to better understand the whole field and take it to the next level.