This paper explores three related themes: the statistical nature of hyperspectral background clutter; why should it be like this; and how to exploit it in algorithms. We begin by reviewing the evidence for the non-Gaussian and in particular fat-tailed nature of hyperspectral background distributions. Following this we develop a simple statistical model that gives some insight into why the observed fat tails occur. We demonstrate that this model fits the background data for some hyperspectral data sets. Finally we make use of the model to develop hyperspectral detection algorithms and compare them to traditional algorithms on some real world data sets.