Novel adsorbents with a simple preparation process and large capacity for removing highly toxic and nondegradable heavy metals from water have drawn the attention of researchers. Electrospun nanofiber membranes usually have the advantages of large specific surface areas and high porosity and allowing flexible control and easy functionalization. These membranes show remarkable application potential in the field of heavy metal wastewater treatment. In this paper, the electrospinning technologies, process types, and the structures and types of nanofibers that can be prepared are reviewed, and the relationships among process, structure and properties are discussed. On one hand, based on the different components of electrospun nanofibers, the use of organic, inorganic and organic−inorganic nanofiber membrane adsorbents in heavy metal wastewater treatment are introduced, and their advantages and future development are summarized and prospected. On the other hand, based on the microstructure and overall structure of the nanofiber membrane, the recent progresses of electrospun functional membranes for heavy metal removal are reviewed, and the advantages of different structures for applications are concluded. Overall, this study lays the foundation for future research aiming to provide more novel structured adsorbents.