Studies on radiative transfer lead to a clean formulation of polarised photon transport in terms of the vector Boltzmann-Chandrasekhar equation whose solution gives the four Stokes components of the flux, from which the full polarisation state of the photons can be determined at any given position, wavelength (energy) and solid angle. One of the relevant results observed during the formulation of the vector transport equation is the partial coverage of the wave properties of the photons with this model. In fact, even if the Boltzmann-Chandrasekhar vector equation is an important step forward for the description of radiative transfer with respect to the scalar approach used to describe “particle”-like photons, it is still insufficient to provide a whole description of an important phase-related property like coherence. In this sense, the above vector equation seems to be appropriate for describing photon beams which add incoherently among them, but not yet for describing coherent interference. In this article, it will be given a summarised view of the evolution of the Boltzmann transport equation from scalar to vector first, making possible the description of the evolution of the polarisation state. Then, it will be illustrated the state-of-the-art of the transport codes developed at Bologna based on this model. Finally, the application of the codes will be shown with some examples.