There is a growing need to monitor anthropogenic organic contaminants detected in water sources. DNA aptamers are synthetic single-stranded oligonucleotides, selected to bind to target contaminants with favorable selectivity and sensitivity. These aptamers can be functionalized and are used with a variety of sensing platforms to develop sensors, or aptasensors. In this critical review, we (1) identify the state-of-the-art in DNA aptamer selection, (2) evaluate target and aptamer properties that make for sensitive and selective binding and sensing, (3) determine strengths and weaknesses of alternative sensing platforms, and (4) assess the potential for aptasensors to quantify environmentally relevant concentrations of organic contaminants in water. Among a suite of target and aptamer properties, binding affinity is either directly (e.g., organic carbon partition coefficient) or inversely (e.g., polar surface area) correlated to properties that indicate greater target hydrophobicity results in the strongest binding aptamers, and binding affinity is correlated to aptasensor limits of detection. Electrochemical-based aptasensors show the greatest sensitivity, which is similar to ELISA-based methods. Only a handful of aptasensors can detect organic pollutants at environmentally relevant concentrations, and interference from structurally similar analogs commonly present in natural waters is a yet-to-be overcome challenge. These findings lead to recommendations to improve aptasensor performance.