  We discuss recent work showing that in certain cases the membrane paradigm
equations governing the dynamics of black hole horizons can be recast as
relativistic conservation law equations. In the context of gauge/gravity
dualities, these equations are interpreted as defining the viscous
hydrodynamics of a holographically dual relativistic field theory. Using this
approach, one can derive the viscous transport coefficients and the form of the
entropy current for field theories dual to gravity plus matter fields.
