We review recent developments in special geometry, emphasizing the role of
real coordinates. In the first part we discuss the para-complex geometry of
vector and hypermultiplets in rigid Euclidean N=2 supersymmetry. In the second
part we study the variational principle governing the near horizon limit of BPS
black holes in matter-coupled N=2 supergravity and observe that the black hole
entropy is the Legendre transform of the Hesse potential encoding the geometry
of the scalar fields.Comment: 27 pages, contributed to the Handbook on Pseudo-Riemannian Geometry
and Supersymmetr
