Black hole entropy, special geometry and strings

We review work done over the last years on the macroscopic and microscopic entropy of supersymmetric black holes in fourdimensional N = 2 supergravity and in N = 2 compactifications of string theory and M-theory. Particular e mphasis is put on the crucial role of higher curvature terms and of modific ations of the area law in obtaining agreement between the macroscopic entro py, which is a geometric property of black hole solutions and the microscop ic entropy, which is computed by state counting in Calabi-Yau compactificat ions of string or M-theory. We also discuss invariance properties of the en tropy under stringy T-duality and S-duality transformations in N = 2.4 comp actifications in presence of higher curvature terms. In order to make the paper self-contained ws review the laws of black hole mechanics in higher derivative gravity, the definition of entropy as a surf ace charge, the superconformal off-shell description of N = 2 supergravity, special geometry, and N = 2 compactifications of heterotic and type II str ing theory and of M-theory.