Heavy metals (HMs) are persistent and toxic environmental pollutants that pose critical risks toward human health and environmental safety. Their efficient elimination from water and wastewater is essential to protect public health, ensure environmental safety, and enhance sustainability. In the recent decade, nanomaterials have been developed extensively for rapid and effective removal of HMs from water and wastewater and to address the certain economical and operational challenges associated with conventional treatment practices, including chemical precipitation, ion exchange, adsorption, and membrane separation. However, the complicated and expensive manufacturing process of nanoparticles and nanotubes, their reduced adsorption capacity due to the aggregation, and challenging recovery from aqueous solutions limited their widespread applications for HM removal practices. Thus, the nanofibers have emerged as promising adsorbents due to their flexible and facile production process, large surface area, and simple recovery. A growing number of chemical modification methods have been devised to promote the nanofibers' adsorption capacity and stability within the aqueous systems. This paper briefly discusses the challenges regarding the effective and economical application of conventional treatment practices for HM removal. It also identifies the practical challenges for widespread applications of nanomaterials such as nanoparticles and nanotubes as HMs adsorbents. This paper focuses on nanofibers as promising HMs adsorbents and reviews the most recent advances in terms of chemical grafting of nanofibers, using the polymers blend, and producing the composite nanofibers to create highly effective and stable HMs adsorbent materials. Furthermore, the parameters that influence the HM removal by electrospun nanofibers and the reusability of adsorbent nanofibers were discussed. Future research needs to address the gap between laboratory investigations and commercial applications of adsorbent nanofibers for water and wastewater treatment practices are also presented.