Black Hole Entropy: Departures from Area Law

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.