We consider the effect of back reaction of quantized massive fields on the metric of extreme black holes (EBH's). We find the analytical approximate expression for the stress-energy tensor for a scalar (with an arbitrary coupling), spinor and vector fields near an event horizon. We show that, independent of a concrete type of EBH, the energy measured by a freely falling observer is finite on the horizon, so that quantum back reaction is consistent with the existence of EBH's. For the Reissner-Nordstrom EBH with a total mass M-tot and charge Q we show that for all cases of physical interest M-tot < Q. We also discuss different types of quantum-corrected Bertotti-Robinson spacetimes, find for them exact self-consistent solutions, and consider situations in which tiny quantum corrections lead to the qualitative change of the classical geometry and topology. In all cases one should start not from a classical background with further added quantum corrections but from the quantum-corrected self-consistent geometries from the very beginning.
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