The measured Mueller matrices contain up to 16 independent parameters for each measurement configuration (spectral profile of the wave probe of the polarimeter, angle of incidence, observation direction, etc.) and for each spatially resolved element of the sample (imaging polarimetry). Thus, the polarimetric techniques are widely used for the study of a great variety of material samples in optics and remote sensing. Nevertheless, the relevant physical information does not appear explicitly in the measured parameters, and thus, the best knowledge of the structure of the physical information contained in a Mueller matrix is required in order to develop appropriate procedures for the polarimetric analysis. The main approaches for serial and parallel decompositions as well as for the geometric representation of measured Mueller matrices are reviewed. Furthermore, the physically invariant polarimetric quantities are identified and decoupled.