Recent advances in the understanding of the origin of the notorious residual n-type conductivity in GaN and our new concept of co-doping for improved p-type conductivity in GaN are briefly reviewed. Our experimental data reveal that O from residual H2O, which substitutes N on lattice sites, is the origin for the observed n-type conductivity. Go-doping with Be and O to form donor-accepted pairs in GaN results in a strongly improved p-type conductivity at room temperature due to a substantial enhancement of the hole mobility. This concept has been independently confirmed by theoretical calculations.