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{\large\bf Scaling Theory of the Quantum Hall Effect} \\

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Bodo Huckestein\\

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{\small{\em
Institut f\"ur Theoretische Physik, Universit\"at zu K\"oln, D-50937 K\"oln, Germany}} \\

{\tt bh@thp.uni-koeln.de}
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The transitions between different plateaus with quantized values of
the Hall conductivity are among the best studied examples of quantum
phase transitions. The transitions are driven by a change in the
filling factor of the two-dimensional electron or hole gas. Both in
experiment and in numerical simulations, scaling behavior as a
function of magnetic field, system size, temperature, and frequency
has been observed near the transitions. At the transitions,
strong, multifractal fluctuations of local quantities are expected. 

The status of our understanding of the plateau transitions is reviewed 
and some open problems, like the vanishing of the quantum Hall effect at 
low magnetic fields, are discussed.

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