  We develop and significantly generalize the effective worldvolume theory for
higher-dimensional black holes recently proposed by the authors. The theory,
which regards the black hole as a black brane curved into a submanifold of a
background spacetime -a blackfold-, can be formulated in terms of an effective
fluid that lives on a dynamical worldvolume. Thus the blackfold equations split
into intrinsic (fluid-dynamical) equations, and extrinsic (generalized geodesic
embedding) equations. The intrinsic equations can be easily solved for
equilibrium configurations, thus providing an efficient formalism for the
approximate construction of novel stationary black holes. Furthermore, it is
possible to study time evolution. In particular, the long-wavelength component
of the Gregory-Laflamme instability of black branes is obtained as a sound-mode
instability of the effective fluid. We also discuss action principles,
connections to black hole thermodynamics, and other consequences and possible
extensions of the approach. Finally, we outline how the fluid/AdS-gravity
correspondence is related to this formalism.
