One hundred years after Einstein formulated General Relativity, the pivotal role of its most fundamental and fascinating objects --- the black holes --- is nowadays recognized in many areas of physics, even beyond astrophysics and cosmology. Still, solving the theory that governs their dynamics remains a formidable challenge that continues to demand new ideas. From many points of view, it is natural to consider the number of spacetime dimensions, D, as an adjustable parameter in the theory. Then we can use it for a perturbative expansion around the limit of very many dimensions, that is, considering 1/D as a small number. In this limit the gravitational field of a black hole is strongly localized close to the horizon and this allows to obtain a new kind of effective theory for black holes. In particular, static black holes follow the same equations that describe soap bubbles. I'll finish discussing the prospects for a reformulation of General Relativity in which black holes are the basic (extended) objects.
