Properties of extremal and supersymmetric horizons

String theory and holography have been able to provide the microstates accounting for the entropy of supersymmetric and extremal black objects, such as black holes and black strings. Gauged supergravity in different spacetime dimensions allows for rotating, charged black objects displaying inner horizons, in addition to the outer event horizon. The product of the areas of these horizons has been shown to depend on angular momenta and electric charges, but not on the mass. The thesis studies these features both from first principles and in concrete examples. The main aim is to implement the extremal and supersymmetric limit of the black hole thermodynamics. It is found that in this limit the area product formulae reproduce certain relations between the conserved charges that have been emphasized recently. A key role is played by the recently discovered extremization principle for the black hole thermodynamics in the supersymmetric and extremal limit. We show that this in fact captures the areas of all horizons as well as the area product formula. We give an explicit proof of these results in the context of black holes in five-dimensional N = 2, U(1)^3 gauged supergravity and four-dimensional N = 2, U(1)^4 gauged supergravity and argue that they hold more generally.