The vectorial properties of light beams, and their interaction with illuminated objects, encode abundant information. The properties of such objects are widely represented via a Mueller matrix. The relationship between the matrix elements and physical structures is not obvious, and the matrix has to be decomposed to reveal the “encoded” information. A newly proposed framework for vectorial metrics not only summarizes certain previous symmetry/asymmetry parameters and enables applications, but also introduces new roles and possibilities for use of the metrics. Further directions range from quantum physics to clinical diagnosis.