The availability of easy-to-use polarimetric equipment has made possible the routine study of a wide range of complex materials and provides a large amount of data, in the form of Mueller matrices, to experimentalists. The problem of the physical interpretation of a measured Mueller matrix is thus of growing importance. In the absence of an electromagnetic model describing it, an experimental Mueller matrix can still be phenomenologically interpreted by decomposing it algebraically into simpler components with straightforward physical meaning. The purpose of the present talk is to introduce several algebraic methods in use and to illustrate them on experimental examples.