Fresh water is one of the most precious resources for our society. As a cause of oxygen depletion, organic pollutants released into water streams from industrial discharges, fertilizers, pesticides, detergents or consumed medicines can raise toxicological concerns due to their long-range transportability, bio-accumulation and degradation into carcinogenic compounds. The Stockholm Convention has named 21 persistent organic pollutants (POP) so far. As opposed to other separation techniques, adsorption, typically performed with activated carbons, offers opportunities to combine low operation costs with high performance as well as fast kinetics of capture if custom-designed with the right choice of adsorbent structure and surface chemistry. Nanofibers possess a higher surface to volume ratio compared to commercial macro-adsorbents, and a higher stability in water than other adsorptive nanostructures, such as loose nanoparticles. This paper highlights the potential of nanofibers in organic pollutant adsorption and thus provides an up-to-date overview of their employment for the treatment of wastewater contaminated by disinfectants and pesticides, which is benchmarked with other reported adsorptive structures. The discussion further investigates the impact of adsorbent pore geometry and surface chemistry on the resulting adsorption performance against specific organic molecules. Finally, insight into the physicochemical properties required for an adsorbent against a targeted pollutant is provided.