A somewhat qualitative review of leakage currents J(V,t) in perovskite oxides is presented. It is stressed that space-charge-limited currents (SCLCs) are not alternatives to ionic conduction, Schottky emission, Poole-Frenkel, or Fowler-Nordheim tunneling, but can occur whenever currents due to any of those mechanisms reach a certain threshold and are no longer limited by the details of the metal electrode-ferroelectric interface. Standard metal-semiconductor band models that exclude surface states fail qualitatively to account for the experimental dependences of leakage currents and breakdown voltages on electrode work function; the correct model is metal-n-p-n-metal, with surface donor-state trapping. A discussion of conduction properties in these materials is presented from an ionic conductor viewpoint.