This report treats detection of targets and anomalies in multi- and hyperspectral imagery. An anomaly is in this context something that does not fit a (spectral) model of the background, for example man-made objects in a natural environment. Anomaly detection has the advantage that it does not require a priori knowledge on what is searched for, and/it has the disadvantage that also subjectively unintresting objects are detected. In contrast to anomaly detection an algorithm for or (signature-based) target detection searches for specific targets with known spectral signatures, for example from a data base. This report describes mathematical models for targets and backgrounds and how they are used for detection algorithms.