  The thermodynamic and euclidean functional integral approaches to black hole
entropy are discussed. The existence of some freedom in the definition of the
entropy is pointed out and the possibility of a departure from the
semiclassical expression discussed in the light of quantum corrections. The
semiclassical area dependence of the entropy of matter in the background of a
black hole is also reviewed and shown to break down in the case of extremal
black holes. The cutoff dependence is shown to be different for the extreme
dilatonic and Reissner - Nordstrom black holes.
