Model evaluations of field-dependent leakage currents in the high-k dielectric oxides HfO2 and ZrO2 are presented. The treatment includes a number of competing transport processes on an equal footing. Our simulation results show that trap-assisted-tunneling, though important, is not the most significant contributor. The combined Poole-Frenkel mechanism with modifications from inelastic trap-related processes dominates at electric fields above 1.5 MV/cm. Our model predictions compare very favorably against the reported experimental data for both HfO2 and ZrO 2. Finally, results obtained from the density functional theory based castep simulator are suggestive of dynamic changes in the net energy levels and the possible formation of a mini-band due to oxygen vacancies.