Techniques for the partial or complete determination of the Mueller matrix of elastic light scattering by a given. sample are reviewed. Important developments include several implementations and applications of the dual-rotating-retarder Mueller-matrix ellipsometer and the addition of imaging, scanning, and spectroscopic capabilities. The use of a multi-channel division-of-amplitude photopolarimeter as a polarization state detector, and the proper modulation (or control) of the polarization state generator have substantially increased the efficiency and speed with which the full Mueller matrix can be measured.