When accounting for heterogeneity and non-Gaussianity of real hyperspectral data, elliptical distributions provide reliable models for background characterization. Through these assumptions, this paper highlights the fact that robust estimation procedures are an interesting alternative to classical methods and can bring some great improvement to the detection process. The goal of this paper is then not only to recall well-known methodologies of target detection but also to propose ways to extend them for taking into account the heterogeneity and non-Gaussianity of the hyperspectral images.