In order to obtain empirical information on the magnetism of the solar transition region we need to measure and interpret the linear polarization produced by scattering processes in FUV and EUV spectral lines. Via the Hanle effect such linear polarization signals are sensitive to the magnetic fields expected for the quiet and active regions of the outer solar atmosphere. For example, the Ly$alpha$ line of H,{sc i} at 1216,AA is mainly sensitive to magnetic strengths between 10 and 100 G. The interpretation of the observed spectral line polarization requires the development of suitable modeling tools. To this end, we have developed a three-dimensional (3D), non-LTE multilevel radiative transfer code for modeling the intensity and linear polarization produced by scattering processes in spectral lines and its modification by the Hanle effect.