I will present the results of our recent theoretical studies of intrinsic electron and hole trapping in amorphous SiO2, HfO2 and Al2O3 films. These materials in a bulk crystalline phase exhibit only hole polarons with trapping energies of about 0.2 eV. Recent experimental evidence suggests that both negative and positive charging can occur in amorphous oxides in much deeper states. To investigate whether such charging can be caused by intrinsic electron and hole trapping, we modelled the behaviour of extra electrons and holes in stoichiometric amorphous SiO2, HfO2 and Al2O3 structures using classical simulations and Density Functional Theory. The results demonstrate that single- and bi-polaron electron and hole states can form in a-SiO2 and a-HfO2, where the effect of local disorder is amplified by polaronic relaxation of amorphous network. Only hole trapping is found in a-Al2O3. Both electron and hole bi-polarons can convert into Frenkel pairs of oxygen vacancies and interstitial oxygen ions. These results broaden the concept of intrinsic polaron trapping to disordered oxides. I will discuss challenges in constructing amorphous structures, predicting polaron trapping and comparing the predicted properties with experiment.