Gianfranco Pacchioni University of Milano-Bicocca Dopants in insulating and semiconducting oxides are of fundamental importance for the design of new materials. In recent years a lot of theoretical and experimental activity has been directed to non-metal doping of technologically important oxides like ZnO, TiO2, MgO, etc. There are several fields of application where N-doped oxide materials play a crucial role. In photocatalysis and solar energy harvesting, N-doping has been intensively studied in order to modify the absorption properties of semiconducting oxides like TiO2 and in particular to improve absorption of visible light photons. N-doping has been proposed as a way to induce p-type conductivity in ZnO or to generate diluted magnetic semiconductors of interest for applications in spintronics. In these systems low levels of N-doping introduce isolated magnetic defect centers that can be characterized theoretically and experimentally by a combined use of Electron Paramagnetic Resonance (EPR) and Density Functional Theory (DFT) calculations [1-6]. At higher N-dopant concentrations the occurrence of a magnetic ordering has been suggested, which implies the existence of magnetic interactions between the isolated defects. DFT has well known problems in describing the localized nature of magnetic impurities in insulators. However, the use of hybrid functionals allows one to properly describe the nature of isolated N-derived defects. On the other hand, no magnetic ordering is predicted at this level of theory and for the dopant concentrations used in experiments. The problems related to the theoretical treatment within DFT of magnetic impurities in insulating and semiconducting oxides are discussed. 1) C. Di Valentin, G. Pacchioni, A. Selloni, “Origin of the different photoactivity of N-doped anatase and rutile TiO2”, Physical Review B, 70, 085116-4 (2004). 2) C. Di Valentin, G. Pacchioni, A. Selloni, S. Livraghi, E. Giamello, “Characterization of paramagnetic species in N-doped TiO2 powders by EPR spectroscopy and DFT calculations”, J. of Physical Chemistry B, 109, 11414-11419 (2005). 3) S. Livraghi, M. C. Paganini, E. Giamello, A. Selloni, C. Di Valentin, G. Pacchioni, “Origin of photo-activity of nitrogen-doped titanium-dioxide under visibile light”, J. American Chemical Society, 128, 15666-15671 (2006). 4) F. Gallino, C. Di Valentin, G. Pacchioni, M. Chiesa, E. Giamello, “Nitrogen doped polycrystalline ZnO. A combined Pulse EPR and DFT study”, J. of Material Chemistry, 20, 689-697 (2010). 5) M. Pesci, F. Gallino, C. Di Valentin, G. Pacchioni, “Nature of defect states in Nitrogen-doped MgO”, J. of Physical Chemistry C, 114, 1350-1356 (2010). 6) F. Napoli, M. Chiesa, E. Giamello, M. Fittipaldi, C. Di Valentin, F. Gallino, G. Pacchioni, “N2? radical anions trapped in bulk polycrystalline MgO”, J. of Physical Chemistry C, 114, 5187-5192 (2010).