A main novel feature of higher-dimensional black holes, compared to four-dimensional ones, is that their horizons can have two characteristic lengths of very different size. This calls for qualitatively new techniques to deal with their physics. I will describe a long-distance effective theory that captures their dynamics at scales much larger than the short scale. The theory regards the black hole as a black brane curved into a submanifold of a background spacetime ---a blackfold--- and is formulated in terms of an effective fluid that lives on a dynamical worldvolume. This approach reveals several new kinds of black holes and solves some outstanding problems, but it also changes our perspective on what should be the aim of the study of higher-dimensional black holes.