The prevalence of organic micropollutants (OMPs) and their persistence in water supplies have raised serious concerns for drinking water safety and public health. Conventional water treatment technologies, including adsorption and biological treatment, are known to be insufficient in treating OMPs and have demonstrated poor selectivity toward a wide range of OMPs. Pressure-driven membrane filtration has the potential to remove many OMPs detected in water with high selectivity as a membrane's molecular weight cutoff (MWCO), surface charge, and hydrophilicity can be easily tailored to a targeted OMP's size, charge and octanol-water partition coefficient (K_ow). Over the past 10 years, polymeric (nano)composite microfiltration (MF), ultrafiltration (UF), and nanofiltration (NF) membranes have been extensively synthesized and studied for their ability to remove OMPs. This review discusses the fate and transport of emerging OMPs in water, an assessment of conventional membrane-based technologies (NF, reverse osmosis (RO), forward osmosis (FO), membrane distillation (MD) and UF membrane-based hybrid processes) for their removal, and a comparison to the state-of-the-art nanoenabled membranes with enhanced selectivity toward specific OMPs in water. Nanoenabled membranes for OMP treatment are further discussed with respect to their permeabilities, enhanced properties, limitations, and future improvements.