Electrospun polymer nanofibers (EPNFs) as one-dimensional nanostructures are characterized by a high surface area-to-volume ratio, high porosity, large number of adsorption sites and high adsorption capacity. These properties nominate them to be used as an effective adsorbent for the removal of water pollutants such as heavy metals, dyes and other pollutants. Organic dyes are considered one of the most hazardous water pollutants due to their toxic effects even at very low concentrations. To overcome this problem, the adsorption technique has proven its high effectiveness towards the removal of such pollutants from aqueous systems. The use of the adsorption technique depends mainly on the properties, efficacy, cost and reusability of the adsorbent. So, the use of EPNFs as adsorbents for dye removal has received increasing attention due to their unique properties, adsorption efficiency and reusability. Moreover, the adsorption efficiency and stability of EPNFs in aqueous media can be improved via their surface modification. This review provides a relevant literature survey over the last two decades on the fabrication and surface modification of EPNFs by an electrospinning technique and their use of adsorbents for the removal of various toxic dyes from contaminated water. Factors affecting the adsorption capacity of EPNFs, the best adsorption conditions and adsorption mechanism of dyes onto the surface of various types of modified EPNFs are also discussed. Finally, the adsorption capacity, isotherm and kinetic models for describing the adsorption of dyes using modified and composite EPNFs are discussed.