We will discuss the relationship between the long range asymptotic potential, the fundamental band gap, and Koopmans' compliance in calculating polaron states in relation to well-studied hole polarons in MgO. We compare the performance of functionals with different fractions of long range exact exchange in calculating trapping energies and optical absorption of [Li]0 and V centres. The results demonstrate the importance of long range exact exchange in simultaneously reproducing the correct band gap as well as satisfying Koopmans' compliance, so as to obtain reliable polaron levels to within 0.2 eV. We then use tuned hybrid functionals to calculate the trapping energies and properties of extra electrons and holes in crystalline and amorphous SiO2, Al2O3, ZnO, and HfO2. The results demonstrate deep hole trapping in all amorphous oxides and electron trapping in oxides with p and d character of the bottom of the conduction band. We discuss the agreement of these predictions with the experimental data.