The structure of accretion discs around (super-)massive black holes is discussed in this contribution with special emphasis on the radiation fields. These are of crucial importance for the understanding of these objects since photons control in most cases not only the temperature distributions but also the pressures and shapes. Recent progress in the modelling of photon fields now provides the means for a much improved understanding of the consequences of the multidimensional structure of the discs as well as of the effects of the strong space time curvature and of the high velocities involved. However, the simultaneous inclusion of the NLTE level populations and of many spectral lines is still a major problem. It is also demonstrated that special and general relativity effects strongly distort the apparent brightness distributions and spectra such accretion discs so that a solution of the inverse problem will be very difficult.