Anomaly detection methods are devoted to target detection schemes in which no a priori information about the spectra of the targets of interest is available. This paper reviews classical anomaly detection schemes such as the widely spread Reed-Xiaoli detector and some of its variations. Moreover, the Mahalanobis distance-based detector, rigorously derived from a Kelly's test-based approach, is analyzed and its exact distribution is derived when both mean vector and covariance matrix are unknown and have to be estimated. Although, most of these techniques are based on Gaussian distribution, we also propose here ways to extend them to non-Gaussian framework. For this purpose, elliptical distributions are considered for background statistical characterization. Through this assumption, this paper describes robust estimation procedures (M-estimators of location and scale) more suitable for non-Gaussian environment. We show that using them as plug-in estimators in anomaly detectors leads to some great improvement in the detection process. Finally, the theoretical contribution is validated through simulations and on real hyperspectral scenes.