Inspired by the extreme wetting states displayed by the natural materials, various techniques have been widely investigated to fabricate superhydrophobic and superhydrophilic surfaces. Electrospinning has gained huge amount of interest as fibers with suitable combination of surface chemistry and surface roughness can be easily obtained. This study provides a comprehensive overview of the progress that has been made on electrospun fibers that display superhydrophobicity, superhydrophilicity or a combination of both. The article discusses various modification techniques that can be implemented to obtain fibers with surface heterogeneity for improving its hydrophobicity or hydrophilicity. Both nanometer size of the fibers and secondary nanoscale structures ensure that the fibers have suitable surface topography to exhibit extreme wetting states. Additionally, for the first time, we critically review and identify the role of intrinsic structures such as crystallinity and chain orientation on the wettability of the fibers. We highlight some new emerging application areas that are being explored using superhydrophobic and superhydrophilic fibers. Further, methods for fabricating smart materials with special wettability are also discussed. Such fibers with special wettability show tremendous promise for water harvesting, unidirectional water collection and oil-water filtration applications.