AbstractWe 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 nVof Abelian vector multiplets, outlining the fundamentals of the special Kähler geometry of the vector multiplets' scalar manifold (of complex dimension nV), and studying the${1 \over 2}$‐BPS attractors, as well as the non‐BPS (non‐supersymmetric) ones with non‐vanishing central charge. For symmetric special Kähler 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.