  We review recent results in the study of attractor horizon geometries (with
non-vanishing Bekenstein-Hawking entropy) of dyonic extremal d=4 black holes in
supergravity. We focus on N=2, d=4 ungauged supergravity coupled to a number
n_{V} of Abelian vector multiplets, outlining the fundamentals of the special
Kaehler geometry of the vector multiplets' scalar manifold (of complex
dimension n_{V}), and studying the 1/2-BPS attractors, as well as the non-BPS
(non-supersymmetric) ones with non-vanishing central charge.
  For symmetric special Kaehler geometries, we present the complete
classification of the orbits in the symplectic representation of the classical
U-duality group (spanned by the black hole charge configuration supporting the
attractors), as well as of the moduli spaces of non-BPS attractors (spanned by
the scalars which are not stabilized at the black hole event horizon).
  Finally, we report on an analogous classification for N>2-extended, d=4
ungauged supergravities, in which also the 1/N-BPS attractors yield a related
moduli space.
