  The entropy and the attractor equations for static extremal black hole
solutions follow from a variational principle based on an entropy function. In
the general case such an entropy function can be derived from the reduced
action evaluated in a near-horizon geometry. BPS black holes constitute special
solutions of this variational principle, but they can also be derived directly
from a different entropy function based on supersymmetry enhancement at the
horizon. Both functions are consistent with electric/magnetic duality and for
BPS black holes their corresponding OSV-type integrals give identical results
at the semi-classical level. We clarify the relation between the two entropy
functions and the corresponding attractor equations for N=2 supergravity
theories with higher-derivative couplings in four space-time dimensions. We
discuss how non-holomorphic corrections will modify these entropy functions.
