We describe coherent Raman scattering in a complete spherical formalism allowing a better understanding of the coherent Raman process with respect to its symmetry properties, which is especially helpful in polarized coherent Raman microscopy. We describe how to build the coherent Raman tensor from spontaneous Raman tensor for crystalline and disordered media. We introduce a distribution function for molecular bonds and show how this distribution function results in a new macroscopic symmetry which can be very different from the symmetry of vibrational modes. Finally, we explicitly show polarization configurations for coherent anti-Stokes Raman scattering to probe specific vibration symmetries in crystalline samples and lipid layers.