We show that it is possible to perform full microscopic calculations of the phonon-assisted and no-phonon radiative transitions in silicon nanocrystals. These are based on a tight-binding Hamiltonian for the electron and electron-phonon part together with a valence force-field model for phonons. We predict an unexpected large broadening of the luminescence peaks attributed to the breaking of bulk selection rules and to multiphonon effects in the acoustic range. We also find that phonon-assisted transitions dominate over the full range of sizes. These results are compared to previous estimates in the effective-mass approximation and are used to discuss available experimental data