Hyperspectral target detection methods have until now progressed mainly on two paths in remote sensing research. The first approach, anomaly detection methods, use the difference of a local region with respect to its neighborhood to analyze the image without using any prior information of the searched target. The second approach on the other hand uses a previously obtained signature of the target, which uniquely represents the target's reflection characteristics with respect to the spectral wavelengths. The signature of the target is matched with the pixels of the acquired image to decide on the existence and location of the searched target. These two approaches provide crucial information to detect oil spills to monitor environmental pollution. In this paper, we aim to use and compare anomaly and signature based target detection approaches for the identification of oil slicks. The study area is selected as the Gulf of Mexico, where one of the worst marine oil spill accidents in the history of the petroleum industry occurred in April 2010. The results indicate that signature based algorithms have a better performance in detecting, locating, and quantifying oil spills compared to the anomaly detection methods. Among the anomaly detection methods, the Gaussian Kernel Reed-Xiaoli (RX) method shows also a close performance to signature based methods, although it requires very long execution times on the down side.